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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 5: Q29 (page 188)

Given: $▱ ABZY$ ; $\bar{AY} ≅ \bar{BX}$ ;
Prove: $∠ 1 ≅ ∠ 2$ and $∠ 1 ≅ ∠ 3$ .

Short Answer

Expert verified

$∠ 1 ≅ ∠ 2$ and $∠ 1 ≅ ∠ 3$

Step by step solution

01

Step 1. Consider the diagram.

Parallelogram ABZY is:

Here, $\bar{A Y} ≅ \bar{B X}$ .

02

Step 2. State the proof.

In $Δ A Y Z$ and $Δ A B Z$ ,

Statement	Reason
$Z B ≅ A B$	The sides of a rhombus are equal.
$∠ 1 ≅ ∠ 3$ …… (1)	Angles opposite to equal sides are equal.
$A Y ∥ B Z$	The opposite sides of a rhombus are parallel and transversal $A Z$ .
$∠ 1 ≅ ∠ 4$ …… (2)	Alternate angles.

From (1) and (2),

$∠ 2 ≅ ∠ 1$

Thus, $∠ 1 ≅ ∠ 2$ and $∠ 1 ≅ ∠ 3$ .

03

Step 3. State the conclusion.

Therefore, $∠ 1 ≅ ∠ 2$ and $∠ 1 ≅ ∠ 3$ (proved).

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Most popular questions from this chapter

For the following figure, if $\bar{W R} ⊥ \bar{C E}$ then name all angles congruent to $∠ R C E$ .

Study the markings on each figure and decide whether ABCD must be a parallelogram. If the answer is yes, state the definition or theorem that applies.

Given: ABCDis a $▱, ∠ A ≅ ∠ E$

Prove: localid="1637661691185" $\bar{A B} ≅ \bar{C E}$

PQRS is a parallelogram. Find the values of a, b, x and y.

State the principal definition or theorem that enables you to deduce, from the information given, that quadrilateral SACK is a parallelogram.

$\bar{S A} ≅ \bar{K C}; \bar{S K} ≅ \bar{A C}$

See all solutions

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