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Geometry

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

$Math Studyset Vaia Explanations$ Math

Student Edition · 227 pages

ISBN: 9780395977279

Chapter 4: Q8. (page 120)

Is the following statement “Corresponding parts of congruent triangles are congruent” based on a definition, postulate, or theorem?

Short Answer

Expert verified

The statement “Corresponding parts of congruent triangles are congruent” is based on the definition.

Step by step solution

01

Step 1. Apply the concept of congruent triangles.

Congruent triangles are triangles that have the same size and shape. This means that the corresponding sides are equal and the corresponding angles are equal.

02

Step 2. Step description.

Since the statement is “Corresponding parts of congruent triangles are congruent” defining the statement is thus the statement based on the definition of a congruent triangle.

03

Step 3. Step description.

Therefore, the statement is based on the definition of congruent triangles.

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Most popular questions from this chapter

Decide whether you can deduce by the SSS, SAS, or ASA postulate that another triangle is congruent to $Δ A B C$ . If so, write the congruence and name the postulate used. If not, write no congruence can be deduced.

Given: $Δ ABC$ in plane M; D not in plane M;

$∠ ACB ≅ ∠ ABC; ∠ DCB ≅ ∠ DBC$

Name a pair of congruent triangles. Prove that your answer is correct.

$A B C D E$ is a regular pentagon and $D E F G$ is a square. Find the measures of $∠ EAF, ∠ AFD$ and $∠ DAF$ .

Suppose you are given a scalene triangle and a point $P$ on some line localid="1648799479069" $l$ . How many triangles are there with one vertex at localid="1648799462577" $P$ , another vertex on localid="1648799472074" $l$ , and each triangle congruent to the given triangle?

In the following figure, the two-triangle shown are congruent. Then explain the following statement.

Deduce that $\bar{D C} ∥ \bar{A B} .$

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