CONGRUENT TRIANGLES Concept 23 Congruence Statement Show that

CONGRUENT TRIANGLES Concept 23

Congruence Statement

Show that the polygons are congruent by identifying all congruent corresponding parts. Then write a congruence statement. 1. 2. Corresponding Sides Corresponding Angles Congruence Statement

Show that the polygons are congruent by identifying all congruent corresponding parts. Then write a congruence statement. 3. ∆FGH≅∆MNL 4. ∆YXZ≅∆CBA Corresponding Sides Corresponding Angles

5 cm

Polygon ABCD ≅ polygon PQRS. 5. List the congruent corresponding parts. Corresponding Angles Corresponding Sides 6. Find the value of x. 7. Find the value of y.

PROVING TRIANGLES ARE CONGRUENT Concept 23 b

REASONS TO USE Vertical Angle Theorem- Any pair of vertical angles are congrue - If there are parallel lines then Alternate Interior Angles Int. Angles are congruent. Alternate Exterior Angles - If there are parallel lines then Alt. Ext. Angles are congruent. - If there are parallel lines then Corresponding Angles are congruent. Right Angles are Congruent - If there are perpendicular lines then Definition of Perpendicular there are right angles.

REASONS TO USE Reflexive Property Symmetric Property Definition of Bisect - To cut down the middle. - Two equal/congruent parts. - If 2 pairs of angles are congruent, then Third Angles Theorem the 3 rd pair is too.

Congruent Sides Congruent Angles All right angles are congruent. Third Angles Theorem Def of Congruent Triangles

Congruent Sides Symmetric Prop. Congruent Angles Alt. Int. Angles Def of Congruent Triangles

Congruent Sides Reflexive Prop. Congruent Angles Def of bisect 3 rd angles thm Def of Congruent Triangles

Statements Reasons 1. Given 2. Def. of bisect 3. Def of bisect 4. Right angles are congruent. 5. 6. 5. Vertical Angles thm 6. 3 rd angles thm 7. Def of Congruent Triangles

Congruent Triangles Shortcuts Concept 24

• Included Angle – an angle that is between two sides of a polygon. (The sides make the angle. ) List included angle for sides AC and BC List the included side for angles B and A. • Included Side – a side that is between two angles of a polygon. (The side is a the common ray between the angles. )

Examples: Naming included angles and included sides.

Examples: Naming included angles and included sides. 3. Name included side for ABD and A. 4. Name included side for D and DCB.

SSS Side-Side

SAS Included Side-Angle-Side

ASA Included Angle-Side-Angle

AAS Angle-Side

HL Hypotenuse-Leg

False Shortcuts

Examples Find which side is needed yet.

5. State third congruence that must be given to prove that ABC DEF using the indicated postulate or theorem.

6. State third congruence that must be given to prove that ABC DEF using the indicated postulate or theorem.

7. State third congruence that must be given to prove that ABC DEF using the indicated postulate or theorem.

8. State third congruence that must be given to prove that ABC DEF using the indicated postulate or theorem.

Examples Find which side is needed yet.

9. State third congruence that must be given to prove that PQR STU using the indicated postulate or theorem. Sketch a picture to support your answer. P Q S R T U

10. State third congruence that must be given to prove that PQR STU using the indicated postulate or theorem. Sketch a picture to support your answer. P Q S R T U

11. State third congruence that must be given to prove that PQR STU using the indicated postulate or theorem. Sketch a picture to support your answer. P Q S R T U

Examples Are they Congruent Triangles

Reflexive Property Symmetric Property Vertical Angles Theorem Alternate Interior Angles Corresponding Angles Right angles are congruent. Third Angles Theorem

12. Is it possible to prove that the triangles are congruent? If there is missing information that can be justified, then state it and it’s reason. Then give the congruence statement and postulate/theorem that supports it. Missing info: Reflexive Prop SSS Postulate

13. Is it possible to prove that the triangles are congruent? If there is missing information that can be justified, then state it and it’s reason. Then give the congruence statement and postulate/theorem that supports it. Missing info: SAS Postulate

14. Is it possible to prove that the triangles are congruent? If there is missing information that can be justified, then state it and it’s reason. Then give the congruence statement and postulate/theorem that supports it. Missing info: Vertical Angle Thm Not congruent because this is side, angle. The angle is not included between the sides.

15. Is it possible to prove that the triangles are congruent? If there is missing information that can be justified, then state it and it’s reason. Then give the congruence statement and postulate/theorem that supports it. Missing info: Vertical Angle Thm ASA Postulate

16. Is it possible to prove that the triangles are congruent? If there is missing information that can be justified, then state it and it’s reason. Then give the congruence statement and postulate/theorem that supports it. Missing info: Reflexive Prop AAS Theorem

17. Is it possible to prove that the triangles are congruent? If there is missing information that can be justified, then state it and it’s reason. Then give the congruence statement and postulate/theorem that supports it. Missing info: Symmetric Prop. T R Q S Q AAS Theorem S

18. Is it possible to prove that the triangles are congruent? If there is missing information that can be justified, then state it and it’s reason. Then give the congruence statement and postulate/theorem that supports it. W V Z Missing info: Reflexive Prop. U X AAS Theorem

19. Is it possible to prove that the triangles are congruent? If there is missing information that can be justified, then state it and it’s reason. Then give the congruence statement and postulate/theorem that supports it. Missing info: Corresponding Angles SAS Theorem

20. Is it possible to prove that the triangles are congruent? If there is missing information that can be justified, then state it and it’s reason. Then give the congruence statement and postulate/theorem that supports it. Missing info: SAS Theorem