Log In Start studying!

Select your language

Suggested languages for you:

Americas

English (US)

Europe

Q1.

Expert-verified

Geometry

Found in: Page 129

Book edition Student Edition

Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

Pages 227 pages

ISBN 9780395977279

Answers without the blur.

Just sign up for free and you're in.

Register for Free I’ll do it later

Short Answer

Describe your plan for proving the following.
1. Given: $\bar{P R}$ bisects $∠ Q P S; \bar{P Q} ≅ \bar{P S}$ Prove: $∠ Q ≅ ∠ S$

$\bar{P R} ≅ \bar{P R}$ (reflexive property)

$∠ Q P R ≅ ∠ S P R$ (bisector of an angle divides it into congruent angles)

$Δ P Q R ≅ Δ S P R$ (SAS congruence criteria)

$∠ Q ≅ ∠ S$ (corresponding parts of congruent triangles)

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1 - Show

According to reflexive property of congruence, a line segment is congruent to itself.

Step 2 - Show ∠QPR≅∠SPR

As bisector of an angle divides it into congruent angles

Step 3 - Show ΔPQR≅ΔPSR

According to SAS congruence criteria, two triangles are said to be congruent if two sides and the included angle of one triangle are congruent to the two sides and the included angle of another triangle

So, from step 1, step 2 and using given

$Δ P Q R ≅ Δ S P R$

Step 4 - Show

As corresponding parts of congruent triangles are equal

Hence, $∠ Q ≅ ∠ S$

Most popular questions for Math Textbooks

For the following figure, does the SAS postulates justify that the two triangles are congruent.

Draw and label a diagram. List, in terms of the diagram, what is given and what is to be proved. Then write a two-column proof.

25. If pentagon $ABCDE$ v is equilateral and has right angles at $B$ and $E$ , then diagonals $\bar{AC}$ and $\bar{AD}$ form congruent triangles.

Plot the given points on graph paper. Draw $Δ FAT$ . Locate point $C$ so that role="math" localid="1638337170606" $Δ FAT ≅ Δ CAT$ .

role="math" localid="1638337180452" $F (7, 5)$ role="math" localid="1638337224388" $A (- 2, 2)$ role="math" localid="1638337234009" $T (5, 2)$

Suppose that $Δ B I G ≅ Δ C A T$ , then complete the following statement.

$__≅ \bar{A T}$

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.

Want to see more solutions like these?

Sign up for free to discover our expert answers

Get Started - It’s free

Recommended explanations on Math Textbooks

94% of StudySmarter users get better grades.

Sign up for free