5 5 Proving Triangles Congruent using SSS Right

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5. 5 Proving Triangles Congruent using SSS. Right Triangle Properties Geometry Besides SAS, What

5. 5 Proving Triangles Congruent using SSS. Right Triangle Properties Geometry Besides SAS, What other ways can you prove triangles congruent?

Goals Use SSS postulate to prove triangles are congruent. n Solve triangle problems. n

Goals Use SSS postulate to prove triangles are congruent. n Solve triangle problems. n Use Hypotenuse-leg Theorem n 30 January 2022 Geometry 5. 5 Proving Triangles Congruent: SSS HL 2

n If three sides of one triangle are congruent to three sides of another

n If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent. B S ABC RST A 30 January 2022 C R Geometry 5. 5 Proving Triangles Congruent: SSS HL T 3

Are these triangles congruent? YES! S S 12 10 S S 10 12 7

Are these triangles congruent? YES! S S 12 10 S S 10 12 7 S 30 January 2022 7 S Why? SSS Geometry 5. 5 Proving Triangles Congruent: SSS HL 4

Prove MAD MAN. A M D N 1. MD MN (Given) 2. AD AN

Prove MAD MAN. A M D N 1. MD MN (Given) 2. AD AN (Given) 3. AM (Reflexive) 4. MAD MAN (SSS) 30 January 2022 Geometry 5. 5 Proving Triangles Congruent: SSS HL 5

Special Case of SSA that works Even though this is SSA, these triangles are

Special Case of SSA that works Even though this is SSA, these triangles are congruent. HL 30 January 2022 Geometry 5. 5 Proving Triangles Congruent: SSS HL 6

Theorem 5. 9 HL (or Hy-Leg) n If the hypotenuse and a leg of

Theorem 5. 9 HL (or Hy-Leg) n If the hypotenuse and a leg of a right triangle are congruent to corresponding parts of another right triangle, then the triangles are congruent. 30 January 2022 Geometry 5. 5 Proving Triangles Congruent: SSS HL 7

Corollary LL (or Leg-Leg) n If the two legs of a right triangle are

Corollary LL (or Leg-Leg) n If the two legs of a right triangle are congruent to corresponding parts of another right triangle, then the triangles are congruent. (This is just SAS. ) 30 January 2022 Geometry 5. 5 Proving Triangles Congruent: SSS HL 8

Example B 50° 10 cm 90° ? A D Is ABD CBD? 10 cm

Example B 50° 10 cm 90° ? A D Is ABD CBD? 10 cm 40° C 1. ABD and CBD are both rt. s. 2. AB = CB (they’re both 10 cm) 3. The triangles share BD. 4. The hypotenuse and leg are congruent ABD CBD by HL. 30 January 2022 Geometry 5. 5 Proving Triangles Congruent: SSS HL 9

One last problem. Solve for x and y. y° x° 50° Solution… 30 January

One last problem. Solve for x and y. y° x° 50° Solution… 30 January 2022 Geometry 5. 5 Proving Triangles Congruent: SSS HL 10

Solution… 80° y° 50° ? 40° x° 50° 70° 60° This triangle is equilateral.

Solution… 80° y° 50° ? 40° x° 50° 70° 60° This triangle is equilateral. Each angle is? 60° These angles form straight angle. The missing angle is? 30 January 2022 Geometry 5. 5 Proving Triangles Congruent: SSS HL 11

Summarize what you learned SSS can be use to prove trianlges congruent. n Two

Summarize what you learned SSS can be use to prove trianlges congruent. n Two right triangles can be proved congruent using HL or LL. n 30 January 2022 Geometry 5. 5 Proving Triangles Congruent: SSS HL 12