Question

Tell which pairs of congruent parts and what method (SSS, ASA, AAS, or HL) you would use to prove the triangles are congruent. Given: $\angle 3 \cong \angle 4 ; \angle 5 \cong \angle 6$ $\triangle Q P Y \cong \triangle T P X$ by what method?

Name: Problem 13, Chapter 4: Geometry
Uploaded: 2019-10-10T03:14:10-08:00
Duration: 15 s
Channel: Amrita Bhasin
Description: Tell which pairs of congruent parts and what method (SSS, ASA, AAS, or HL) you would use to prove the triangles are congruent. Given: ∠3 ≅∠4 ; ∠5 ≅∠6 Q P Y ≅T P X by what method?

   Tell which pairs of congruent parts and what method (SSS, ASA, AAS, or HL) you would use to prove the triangles are congruent.
Given: $\angle 3 \cong \angle 4 ; \angle 5 \cong \angle 6$
$\triangle Q P Y \cong \triangle T P X$ by what method?

Geometry

Ray C.… 1st Edition

Chapter 4, Problem 13

Instant Answer

Solved by Expert Amrita Bhasin

10/10/2019

Step 1

Step 1: Given that $\angle 3 \cong \angle 4$ and $\angle 5 \cong \angle 6$, we can say that $\angle QPY \cong \angle TPX$ and $\angle PQY \cong \angle PTX$. Show more…

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Tell which pairs of congruent parts and what method (SSS, ASA, AAS, or HL) you would use to prove the triangles are congruent. Given: $\angle 3 \cong \angle 4 ; \angle 5 \cong \angle 6$ $\triangle Q P Y \cong \triangle T P X$ by what method?

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Key Concepts

Triangle Congruence Criteria

The triangle congruence criteria are a set of methods used to show that two triangles are identical in shape and size. They include SSS (Side-Side-Side), ASA (Angle-Side-Angle), AAS (Angle-Angle-Side), and HL (Hypotenuse-Leg for right triangles). Each method provides a sufficient condition for proving triangle congruence when the specified parts of one triangle can be shown to correspond exactly with the parts of another triangle.

Angle-Side-Angle (ASA) Congruence

The ASA congruence criterion states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. The problem gives us two pairs of congruent angles, and the between them is typically the shared side. This method is essential when the side connecting the two angles is known to be congruent, directly leading to triangle congruence.

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