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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: Q10. (page 142)

For each diagram, name a pair of overlapping triangles. Tell whether the triangles are congruent by the $S S S, S A S, A S A, A A S, or H L$ method.
10. Given: $\overset{炉}{AB} 鈮� \overset{炉}{DC}; \overset{炉}{AC} 鈮� \overset{炉}{DB}$

Short Answer

Expert verified

The pair of overlapping triangles that are congruent are $鈻� ABC$ and $鈻� DCB$ .

The triangles $鈻� A B C$ and $鈻� D C B$ are congruent by the SSS method.

Step by step solution

01

- Observe the given diagram.

The given diagram is:

02

- Description of step.

It is being given that $\overset{炉}{A B} 鈮� \overset{炉}{D C}$ and $\overset{炉}{A C} 鈮� \overset{炉}{D B}$ .

In the triangles $鈻� A B C$ and $鈻� D C B$ , the side that is common is $B C$ .

Therefore, $\overset{炉}{B C} 鈮� \overset{炉}{B C}$ by using the reflexive property.

In the triangles $鈻� A B C$ and $鈻� D C B$ , it can be noticed that $\overset{炉}{A B} 鈮� \overset{炉}{D C}, \overset{炉}{B C} 鈮� \overset{炉}{B C}$ and $\overset{炉}{A C} 鈮� \overset{炉}{D B}$ .

Therefore, the triangles $鈻� A B C$ and $鈻� D C B$ are the congruent triangles by using the $S S S$ method.

03

- Write the conclusion.

The pair of overlapping triangles that are congruent are $鈻� A B C$ and $鈻� D C B$ .

The triangles $鈻� A B C$ and $鈻� D C B$ are congruent by the SSS method.

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Most popular questions from this chapter

Describe your plan for proving the following.

1. Given: $\overset{炉}{P R}$ bisects $鈭� Q P S; \overset{炉}{P Q} 鈮� \overset{炉}{P S}$ Prove: $鈭� Q 鈮� 鈭� S$

For the following figure, can the triangle be proved congruent? If so, what postulate can be used?

$\overset{炉}{OR}$ is a common side of two congruent quadrilaterals.

Complete: quad. $NERO 鈮�$ quad $\underset{炉}{?}$ .

$\overset{炉}{OR}$ is a common side of two congruent quadrilaterals.

Complete: quad. $NERO 鈮�$ quad $\underset{炉}{?}$ .

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

See all solutions

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