Proving Triangles are Congruent SSS SAS ASA AAS
![Proving Triangles are Congruent SSS, SAS; ASA; AAS CCSS: G. CO 7 Proving Triangles are Congruent SSS, SAS; ASA; AAS CCSS: G. CO 7](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-1.jpg)
![Standards for Mathematical Practices • 1. Make sense of problems and persevere in solving Standards for Mathematical Practices • 1. Make sense of problems and persevere in solving](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-2.jpg)
![CCSS: G. CO 7 • USE the definition of congruence in terms of rigid CCSS: G. CO 7 • USE the definition of congruence in terms of rigid](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-3.jpg)
![ESSENTIAL QUESTION • How do we show that triangles are congruent? • How do ESSENTIAL QUESTION • How do we show that triangles are congruent? • How do](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-4.jpg)
![Objectives: 1. Prove that triangles are congruent using the ASA Congruence Postulate and the Objectives: 1. Prove that triangles are congruent using the ASA Congruence Postulate and the](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-5.jpg)
![Proving Triangles are Congruent: SSS and SAS Proving Triangles are Congruent: SSS and SAS](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-6.jpg)
![SSS AND SAS CONGRUENCE POSTULATES If all six pairs of corresponding parts (sides and SSS AND SAS CONGRUENCE POSTULATES If all six pairs of corresponding parts (sides and](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-7.jpg)
![SSS AND SAS CONGRUENCE POSTULATES POSTULATE 19 Side - Side (SSS) Congruence Postulate If SSS AND SAS CONGRUENCE POSTULATES POSTULATE 19 Side - Side (SSS) Congruence Postulate If](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-8.jpg)
![SSS AND SAS CONGRUENCE POSTULATES The SSS Congruence Postulate is a shortcut for proving SSS AND SAS CONGRUENCE POSTULATES The SSS Congruence Postulate is a shortcut for proving](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-9.jpg)
![SSS AND SAS CONGRUENCE POSTULATES POSTULATE 20 Side-Angle-Side (SAS) Congruence Postulate If two sides SSS AND SAS CONGRUENCE POSTULATES POSTULATE 20 Side-Angle-Side (SAS) Congruence Postulate If two sides](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-10.jpg)
![Congruent Triangles in a Coordinate Plane Use the SSS Congruence Postulate to show that Congruent Triangles in a Coordinate Plane Use the SSS Congruence Postulate to show that](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-11.jpg)
![Congruent Triangles in a Coordinate Plane Use the distance formula to find lengths BC Congruent Triangles in a Coordinate Plane Use the distance formula to find lengths BC](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-12.jpg)
![Congruent Triangles in a Coordinate Plane BC = 34 and GH = 34 BC Congruent Triangles in a Coordinate Plane BC = 34 and GH = 34 BC](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-13.jpg)
![SSS postulate SAS postulate SSS postulate SAS postulate](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-14.jpg)
![T S C G The vertex of the included angle is the point T S C G The vertex of the included angle is the point](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-15.jpg)
![SSS postulate Not enough info SSS postulate Not enough info](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-16.jpg)
![SSS postulate SAS postulate SSS postulate SAS postulate](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-17.jpg)
![Not Enough Info SAS postulate Not Enough Info SAS postulate](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-18.jpg)
![SSS postulate Not Enough Info SSS postulate Not Enough Info](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-19.jpg)
![SAS postulate SAS postulate](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-20.jpg)
![Congruent Triangles in a Coordinate Plane Use the SSS Congruence Postulate to show that Congruent Triangles in a Coordinate Plane Use the SSS Congruence Postulate to show that](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-21.jpg)
![Congruent Triangles in a Coordinate Plane Use the distance formula to find lengths PN Congruent Triangles in a Coordinate Plane Use the distance formula to find lengths PN](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-22.jpg)
![Congruent Triangles in a Coordinate Plane PN = 41 and FD = 41 PN Congruent Triangles in a Coordinate Plane PN = 41 and FD = 41 PN](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-23.jpg)
![Proving Triangles are Congruent ASA; AAS Proving Triangles are Congruent ASA; AAS](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-24.jpg)
![Postulate 21: Angle-Side-Angle (ASA) Congruence Postulate • If two angles and the included side Postulate 21: Angle-Side-Angle (ASA) Congruence Postulate • If two angles and the included side](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-25.jpg)
![Theorem 4. 5: Angle-Side (AAS) Congruence Theorem • If two angles and a non-included Theorem 4. 5: Angle-Side (AAS) Congruence Theorem • If two angles and a non-included](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-26.jpg)
![Theorem 4. 5: Angle-Side (AAS) Congruence Theorem Given: A D, C F, BC EF Theorem 4. 5: Angle-Side (AAS) Congruence Theorem Given: A D, C F, BC EF](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-27.jpg)
![Theorem 4. 5: Angle-Side (AAS) Congruence Theorem You are given that two angles of Theorem 4. 5: Angle-Side (AAS) Congruence Theorem You are given that two angles of](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-28.jpg)
![Ex. 1 Developing Proof Is it possible to prove the triangles are congruent? If Ex. 1 Developing Proof Is it possible to prove the triangles are congruent? If](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-29.jpg)
![Ex. 1 Developing Proof A. In addition to the angles and segments that are Ex. 1 Developing Proof A. In addition to the angles and segments that are](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-30.jpg)
![Ex. 1 Developing Proof Is it possible to prove the triangles are congruent? If Ex. 1 Developing Proof Is it possible to prove the triangles are congruent? If](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-31.jpg)
![Ex. 1 Developing Proof B. In addition to the congruent segments that are marked, Ex. 1 Developing Proof B. In addition to the congruent segments that are marked,](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-32.jpg)
![Ex. 1 Developing Proof Is it possible to prove the triangles are congruent? If Ex. 1 Developing Proof Is it possible to prove the triangles are congruent? If](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-33.jpg)
![Ex. 1 Developing Proof The two pairs of parallel sides can be used to Ex. 1 Developing Proof The two pairs of parallel sides can be used to](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-34.jpg)
![Ex. 2 Proving Triangles are Congruent Given: AD ║EC, BD BC Prove: ∆ABD ∆EBC Ex. 2 Proving Triangles are Congruent Given: AD ║EC, BD BC Prove: ∆ABD ∆EBC](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-35.jpg)
![Proof: Statements: 1. BD BC 2. AD ║ EC 3. D C 4. ABD Proof: Statements: 1. BD BC 2. AD ║ EC 3. D C 4. ABD](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-36.jpg)
![Proof: Statements: 1. BD BC 2. AD ║ EC 3. D C 4. ABD Proof: Statements: 1. BD BC 2. AD ║ EC 3. D C 4. ABD](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-37.jpg)
![Proof: Statements: 1. BD BC 2. AD ║ EC 3. D C 4. ABD Proof: Statements: 1. BD BC 2. AD ║ EC 3. D C 4. ABD](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-38.jpg)
![Proof: Statements: 1. BD BC 2. AD ║ EC 3. D C 4. ABD Proof: Statements: 1. BD BC 2. AD ║ EC 3. D C 4. ABD](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-39.jpg)
![Proof: Statements: 1. BD BC 2. AD ║ EC 3. D C 4. ABD Proof: Statements: 1. BD BC 2. AD ║ EC 3. D C 4. ABD](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-40.jpg)
![Proof: Statements: 1. BD BC 2. AD ║ EC 3. D C 4. ABD Proof: Statements: 1. BD BC 2. AD ║ EC 3. D C 4. ABD](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-41.jpg)
![Note: • You can often use more than one method to prove a statement. Note: • You can often use more than one method to prove a statement.](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-42.jpg)
- Slides: 42
![Proving Triangles are Congruent SSS SAS ASA AAS CCSS G CO 7 Proving Triangles are Congruent SSS, SAS; ASA; AAS CCSS: G. CO 7](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-1.jpg)
Proving Triangles are Congruent SSS, SAS; ASA; AAS CCSS: G. CO 7
![Standards for Mathematical Practices 1 Make sense of problems and persevere in solving Standards for Mathematical Practices • 1. Make sense of problems and persevere in solving](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-2.jpg)
Standards for Mathematical Practices • 1. Make sense of problems and persevere in solving them. • 2. Reason abstractly and quantitatively. • 3. Construct viable arguments and critique the reasoning of others. • 4. Model with mathematics. • 5. Use appropriate tools strategically. • 6. Attend to precision. • 7. Look for and make use of structure. • 8. Look for and express regularity in repeated reasoning.
![CCSS G CO 7 USE the definition of congruence in terms of rigid CCSS: G. CO 7 • USE the definition of congruence in terms of rigid](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-3.jpg)
CCSS: G. CO 7 • USE the definition of congruence in terms of rigid motions to SHOW that two triangles ARE congruent if and only if corresponding pairs of sides and corresponding pairs of angles ARE congruent.
![ESSENTIAL QUESTION How do we show that triangles are congruent How do ESSENTIAL QUESTION • How do we show that triangles are congruent? • How do](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-4.jpg)
ESSENTIAL QUESTION • How do we show that triangles are congruent? • How do we use triangle congruence to plane and write proves , and prove that constructions are valid?
![Objectives 1 Prove that triangles are congruent using the ASA Congruence Postulate and the Objectives: 1. Prove that triangles are congruent using the ASA Congruence Postulate and the](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-5.jpg)
Objectives: 1. Prove that triangles are congruent using the ASA Congruence Postulate and the AAS Congruence Theorem 2. Use congruence postulates and theorems in real-life problems.
![Proving Triangles are Congruent SSS and SAS Proving Triangles are Congruent: SSS and SAS](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-6.jpg)
Proving Triangles are Congruent: SSS and SAS
![SSS AND SAS CONGRUENCE POSTULATES If all six pairs of corresponding parts sides and SSS AND SAS CONGRUENCE POSTULATES If all six pairs of corresponding parts (sides and](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-7.jpg)
SSS AND SAS CONGRUENCE POSTULATES If all six pairs of corresponding parts (sides and angles) are congruent, then the triangles are congruent. If Sides are congruent and Angles are congruent 1. AB DE 4. A D 2. BC EF 5. B E 3. AC DF 6. C F then Triangles are congruent ABC DEF
![SSS AND SAS CONGRUENCE POSTULATES POSTULATE 19 Side Side SSS Congruence Postulate If SSS AND SAS CONGRUENCE POSTULATES POSTULATE 19 Side - Side (SSS) Congruence Postulate If](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-8.jpg)
SSS AND SAS CONGRUENCE POSTULATES POSTULATE 19 Side - Side (SSS) Congruence Postulate If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent. If Side S MN QR Side S NP RS Side S PM SQ then MNP QRS
![SSS AND SAS CONGRUENCE POSTULATES The SSS Congruence Postulate is a shortcut for proving SSS AND SAS CONGRUENCE POSTULATES The SSS Congruence Postulate is a shortcut for proving](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-9.jpg)
SSS AND SAS CONGRUENCE POSTULATES The SSS Congruence Postulate is a shortcut for proving two triangles are congruent without using all six pairs of corresponding parts.
![SSS AND SAS CONGRUENCE POSTULATES POSTULATE 20 SideAngleSide SAS Congruence Postulate If two sides SSS AND SAS CONGRUENCE POSTULATES POSTULATE 20 Side-Angle-Side (SAS) Congruence Postulate If two sides](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-10.jpg)
SSS AND SAS CONGRUENCE POSTULATES POSTULATE 20 Side-Angle-Side (SAS) Congruence Postulate If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent. If Side S Angle A Side S PQ WX Q X QS XY then PQS WXY
![Congruent Triangles in a Coordinate Plane Use the SSS Congruence Postulate to show that Congruent Triangles in a Coordinate Plane Use the SSS Congruence Postulate to show that](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-11.jpg)
Congruent Triangles in a Coordinate Plane Use the SSS Congruence Postulate to show that ABC FGH. SOLUTION AC = 3 and FH = 3 AC FH AB = 5 and FG = 5 AB FG
![Congruent Triangles in a Coordinate Plane Use the distance formula to find lengths BC Congruent Triangles in a Coordinate Plane Use the distance formula to find lengths BC](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-12.jpg)
Congruent Triangles in a Coordinate Plane Use the distance formula to find lengths BC and GH. d= BC = (x 2 – x 1 ) 2 + ( y 2 – y 1 ) 2 (– 4 – (– 7)) 2 + (5 – 0 ) 2 d= GH = (x 2 – x 1 ) 2 + ( y 2 – y 1 ) 2 (6 – 1) 2 + (5 – 2 ) 2 = 32 + 52 = 52 + 32 = 34
![Congruent Triangles in a Coordinate Plane BC 34 and GH 34 BC Congruent Triangles in a Coordinate Plane BC = 34 and GH = 34 BC](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-13.jpg)
Congruent Triangles in a Coordinate Plane BC = 34 and GH = 34 BC GH All three pairs of corresponding sides are congruent, ABC FGH by the SSS Congruence Postulate.
![SSS postulate SAS postulate SSS postulate SAS postulate](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-14.jpg)
SSS postulate SAS postulate
![T S C G The vertex of the included angle is the point T S C G The vertex of the included angle is the point](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-15.jpg)
T S C G The vertex of the included angle is the point in common. SAS postulate SSS postulate
![SSS postulate Not enough info SSS postulate Not enough info](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-16.jpg)
SSS postulate Not enough info
![SSS postulate SAS postulate SSS postulate SAS postulate](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-17.jpg)
SSS postulate SAS postulate
![Not Enough Info SAS postulate Not Enough Info SAS postulate](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-18.jpg)
Not Enough Info SAS postulate
![SSS postulate Not Enough Info SSS postulate Not Enough Info](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-19.jpg)
SSS postulate Not Enough Info
![SAS postulate SAS postulate](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-20.jpg)
SAS postulate
![Congruent Triangles in a Coordinate Plane Use the SSS Congruence Postulate to show that Congruent Triangles in a Coordinate Plane Use the SSS Congruence Postulate to show that](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-21.jpg)
Congruent Triangles in a Coordinate Plane Use the SSS Congruence Postulate to show that NMP DEF. SOLUTION MN = 4 and DE = 4 MN DE PM = 5 and FE = 5 PM FE
![Congruent Triangles in a Coordinate Plane Use the distance formula to find lengths PN Congruent Triangles in a Coordinate Plane Use the distance formula to find lengths PN](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-22.jpg)
Congruent Triangles in a Coordinate Plane Use the distance formula to find lengths PN and FD. d= PN = (x 2 – x 1 ) 2 + ( y 2 – y 1 ) 2 (– 1 – (– 5)) 2 + (6 – 1 ) 2 d= FD = (x 2 – x 1 ) 2 + ( y 2 – y 1 ) 2 (2 – 6) 2 + (6 – 1 ) 2 = 42 + 52 = (-4) 2 + 5 2 = 41
![Congruent Triangles in a Coordinate Plane PN 41 and FD 41 PN Congruent Triangles in a Coordinate Plane PN = 41 and FD = 41 PN](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-23.jpg)
Congruent Triangles in a Coordinate Plane PN = 41 and FD = 41 PN FD All three pairs of corresponding sides are congruent, NMP DEF by the SSS Congruence Postulate.
![Proving Triangles are Congruent ASA AAS Proving Triangles are Congruent ASA; AAS](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-24.jpg)
Proving Triangles are Congruent ASA; AAS
![Postulate 21 AngleSideAngle ASA Congruence Postulate If two angles and the included side Postulate 21: Angle-Side-Angle (ASA) Congruence Postulate • If two angles and the included side](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-25.jpg)
Postulate 21: Angle-Side-Angle (ASA) Congruence Postulate • If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the triangles are congruent.
![Theorem 4 5 AngleSide AAS Congruence Theorem If two angles and a nonincluded Theorem 4. 5: Angle-Side (AAS) Congruence Theorem • If two angles and a non-included](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-26.jpg)
Theorem 4. 5: Angle-Side (AAS) Congruence Theorem • If two angles and a non-included side of one triangle are congruent to two angles and the corresponding nonincluded side of a second triangle, then the triangles are congruent.
![Theorem 4 5 AngleSide AAS Congruence Theorem Given A D C F BC EF Theorem 4. 5: Angle-Side (AAS) Congruence Theorem Given: A D, C F, BC EF](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-27.jpg)
Theorem 4. 5: Angle-Side (AAS) Congruence Theorem Given: A D, C F, BC EF Prove: ∆ABC ∆DEF
![Theorem 4 5 AngleSide AAS Congruence Theorem You are given that two angles of Theorem 4. 5: Angle-Side (AAS) Congruence Theorem You are given that two angles of](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-28.jpg)
Theorem 4. 5: Angle-Side (AAS) Congruence Theorem You are given that two angles of ∆ABC are congruent to two angles of ∆DEF. By the Third Angles Theorem, the third angles are also congruent. That is, B E. Notice that BC is the side included between B and C, and EF is the side included between E and F. You can apply the ASA Congruence Postulate to conclude that ∆ABC ∆DEF.
![Ex 1 Developing Proof Is it possible to prove the triangles are congruent If Ex. 1 Developing Proof Is it possible to prove the triangles are congruent? If](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-29.jpg)
Ex. 1 Developing Proof Is it possible to prove the triangles are congruent? If so, state the postulate or theorem you would use. Explain your reasoning.
![Ex 1 Developing Proof A In addition to the angles and segments that are Ex. 1 Developing Proof A. In addition to the angles and segments that are](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-30.jpg)
Ex. 1 Developing Proof A. In addition to the angles and segments that are marked, EGF JGH by the Vertical Angles Theorem. Two pairs of corresponding angles and one pair of corresponding sides are congruent. You can use the AAS Congruence Theorem to prove that ∆EFG ∆JHG.
![Ex 1 Developing Proof Is it possible to prove the triangles are congruent If Ex. 1 Developing Proof Is it possible to prove the triangles are congruent? If](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-31.jpg)
Ex. 1 Developing Proof Is it possible to prove the triangles are congruent? If so, state the postulate or theorem you would use. Explain your reasoning.
![Ex 1 Developing Proof B In addition to the congruent segments that are marked Ex. 1 Developing Proof B. In addition to the congruent segments that are marked,](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-32.jpg)
Ex. 1 Developing Proof B. In addition to the congruent segments that are marked, NP NP. Two pairs of corresponding sides are congruent. This is not enough information to prove the triangles are congruent.
![Ex 1 Developing Proof Is it possible to prove the triangles are congruent If Ex. 1 Developing Proof Is it possible to prove the triangles are congruent? If](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-33.jpg)
Ex. 1 Developing Proof Is it possible to prove the triangles are congruent? If so, state the postulate or theorem you would use. Explain your reasoning. UZ ║WX AND UW ║WX. 1 2 3 4
![Ex 1 Developing Proof The two pairs of parallel sides can be used to Ex. 1 Developing Proof The two pairs of parallel sides can be used to](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-34.jpg)
Ex. 1 Developing Proof The two pairs of parallel sides can be used to show 1 3 and 2 4. Because the included side WZ is congruent to itself, ∆WUZ ∆ZXW by the ASA Congruence Postulate. 1 2 3 4
![Ex 2 Proving Triangles are Congruent Given AD EC BD BC Prove ABD EBC Ex. 2 Proving Triangles are Congruent Given: AD ║EC, BD BC Prove: ∆ABD ∆EBC](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-35.jpg)
Ex. 2 Proving Triangles are Congruent Given: AD ║EC, BD BC Prove: ∆ABD ∆EBC Plan for proof: Notice that ABD and EBC are congruent. You are given that BD BC. Use the fact that AD ║EC to identify a pair of congruent angles.
![Proof Statements 1 BD BC 2 AD EC 3 D C 4 ABD Proof: Statements: 1. BD BC 2. AD ║ EC 3. D C 4. ABD](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-36.jpg)
Proof: Statements: 1. BD BC 2. AD ║ EC 3. D C 4. ABD EBC 5. ∆ABD ∆EBC Reasons: 1.
![Proof Statements 1 BD BC 2 AD EC 3 D C 4 ABD Proof: Statements: 1. BD BC 2. AD ║ EC 3. D C 4. ABD](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-37.jpg)
Proof: Statements: 1. BD BC 2. AD ║ EC 3. D C 4. ABD EBC 5. ∆ABD ∆EBC Reasons: 1. Given
![Proof Statements 1 BD BC 2 AD EC 3 D C 4 ABD Proof: Statements: 1. BD BC 2. AD ║ EC 3. D C 4. ABD](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-38.jpg)
Proof: Statements: 1. BD BC 2. AD ║ EC 3. D C 4. ABD EBC 5. ∆ABD ∆EBC Reasons: 1. Given 2. Given
![Proof Statements 1 BD BC 2 AD EC 3 D C 4 ABD Proof: Statements: 1. BD BC 2. AD ║ EC 3. D C 4. ABD](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-39.jpg)
Proof: Statements: 1. BD BC 2. AD ║ EC 3. D C 4. ABD EBC 5. ∆ABD ∆EBC Reasons: 1. Given 2. Given 3. Alternate Interior Angles
![Proof Statements 1 BD BC 2 AD EC 3 D C 4 ABD Proof: Statements: 1. BD BC 2. AD ║ EC 3. D C 4. ABD](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-40.jpg)
Proof: Statements: 1. BD BC 2. AD ║ EC 3. D C 4. ABD EBC 5. ∆ABD ∆EBC Reasons: 1. Given 2. Given 3. Alternate Interior Angles 4. Vertical Angles Theorem
![Proof Statements 1 BD BC 2 AD EC 3 D C 4 ABD Proof: Statements: 1. BD BC 2. AD ║ EC 3. D C 4. ABD](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-41.jpg)
Proof: Statements: 1. BD BC 2. AD ║ EC 3. D C 4. ABD EBC 5. ∆ABD ∆EBC Reasons: 1. Given 2. Given 3. Alternate Interior Angles 4. Vertical Angles Theorem 5. ASA Congruence Theorem
![Note You can often use more than one method to prove a statement Note: • You can often use more than one method to prove a statement.](https://slidetodoc.com/presentation_image_h/e00726e35fa22e2e1071596deb4c580e/image-42.jpg)
Note: • You can often use more than one method to prove a statement. In Example 2, you can use the parallel segments to show that D C and A E. Then you can use the AAS Congruence Theorem to prove that the triangles are congruent.
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