Q13. Tell which pairs of congruent pa... [FREE SOLUTION]

91影视

Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 227 pages

ISBN: 9780395977279

Chapter 4: Q13. (page 144)

Tell which pairs of congruent parts and what methods (SSS, SAS, ASA, AAS, or HL) you would use to prove the triangles are congruent.
Given: $鈭� 3 鈮� 鈭� 4$ ; $鈭� 5 鈮� 鈭� 6$
$鈻� QPY 鈮� 鈻� TPX$ by what method?

Short Answer

Expert verified

The congruent parts in the triangles $鈻� Q P Y$ and $鈻� T P X$ are:

$鈭� PQY 鈮� 鈭� PTX$ , $鈭� PXT 鈮� 鈭� PYQ$ and $PQ 鈮� PT$ .

The triangles $鈻� Q P Y$ and $鈻� T P X$ are congruent by AAS postulate.

Step by step solution

Step 1. Observe the given diagram.

The given diagram is:

Step 2. Write the theorem 4-2.

The theorem 4-2 states that if two angles of a triangle are congruent, then the sides opposite to those angles are congruent.

Step 3. Description of step.

As, $鈭� 3 鈮� 鈭� 4$ , therefore by using the theorem 4-2, it can be said that sides $P Q$ and $P T$ are congruent sides.

Therefore, $P Q 鈮� P T$ .

It is also given that $鈭� 5 鈮� 鈭� 6$ .

In the triangles $鈻� Q P Y$ and $鈻� T P X$ , it can be noticed that $鈭� 3 鈮� 鈭� 4$ , $鈭� 5 鈮� 鈭� 6$ and $P Q 鈮� P T$ .

Therefore, in the triangles $鈻� Q P Y$ and $鈻� T P X$ , it can be noticed that $鈭� P Q Y 鈮� 鈭� P T X$ , $鈭� P X T 鈮� 鈭� P Y Q$ and $P Q 鈮� P T$

Therefore, the triangles $鈻� Q P Y$ and $鈻� T P X$ are the congruent triangles by using the AAS postulate.

Step 4. Write the conclusion.

The postulate that proves the triangles $鈻� Q P Y$ and $鈻� T P X$ are congruent is AAS postulate.

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91影视

Tell which pairs of congruent parts and what methods (SSS, SAS, ASA, AAS, or HL) you would use to prove the triangles are congruent.
Given: $鈭� 3 鈮� 鈭� 4$ ; $鈭� 5 鈮� 鈭� 6$
$鈻� QPY 鈮� 鈻� TPX$ by what method?

Short Answer

Step by step solution

Step 1. Observe the given diagram.

Step 2. Write the theorem 4-2.

Step 3. Description of step.

Step 4. Write the conclusion.

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91影视

Tell which pairs of congruent parts and what methods (SSS, SAS, ASA, AAS, or HL) you would use to prove the triangles are congruent.Given: 鈭�3鈮�鈭�4;鈭�5鈮�鈭�6鈻�QPY鈮�鈻�TPXby what method?

Short Answer

Step by step solution

Step 1. Observe the given diagram.

Step 2. Write the theorem 4-2.

Step 3. Description of step.

Step 4. Write the conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Theoretical and Mathematical Physics

Probability and Statistics

Discrete Mathematics

Mechanics Maths

Geometry

Study anywhere. Anytime. Across all devices.

Tell which pairs of congruent parts and what methods (SSS, SAS, ASA, AAS, or HL) you would use to prove the triangles are congruent.
Given: $鈭� 3 鈮� 鈭� 4$ ; $鈭� 5 鈮� 鈭� 6$
$鈻� QPY 鈮� 鈻� TPX$ by what method?