Chapter 4: Q12. (page 131)

Given: $\bar{W X} ⊥ \bar{U V}; \bar{W X} ⊥ \bar{Y Z}; \bar{W U} ≅ \bar{W V}$
Prove whatever you can about angles 1,2,3, and 4

Short Answer

Expert verified

Statements which can be proved are $∠ 1 ≅ ∠ 2$ and $∠ 3 ≅ ∠ 4$

Step by step solution

Step 1. Show that ΔUWX≅ΔVWX.

By reflexive property of congruence,a side is congruent to itself

So, $\bar{W X} ≅ \bar{W X}$

Also using given $m ∠ 5 = m ∠ 6 = 90 °$

Thus, $Δ U W X ≅ Δ V W X$ by SAS (Side-Angle-Side) congruency criteria

Step 2. Show that ∠3≅∠4.

Since, corresponding parts of congruent triangles are congruent

So, $∠ 3 ≅ ∠ 4$

Step 3. Show that ∠1≅∠2.

Using given statement

$m ∠ W X Y = m ∠ W X Z = 90 °$

Thus, $∠ 1 + ∠ 3 ≅ ∠ 2 + ∠ 4$

Substitute $∠ 3$ for $∠ 4$ in this equation

$\begin{matrix} ∠ 1 + ∠ 3 ≅ ∠ 2 + ∠ 3 \\ ∠ 1 ≅ ∠ 2 \end{matrix}$

Thus, statements which can be proved are $∠ 1 ≅ ∠ 2$ and $∠ 3 ≅ ∠ 4$

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Given: $\bar{W X} ⊥ \bar{U V}; \bar{W X} ⊥ \bar{Y Z}; \bar{W U} ≅ \bar{W V}$
Prove whatever you can about angles 1,2,3, and 4

Short Answer

Step by step solution

Step 1. Show that ΔUWX≅ΔVWX.

Step 2. Show that ∠3≅∠4.

Step 3. Show that ∠1≅∠2.

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Given:WX¯⊥UV¯;WX¯⊥YZ¯;WU¯≅WV¯Prove whatever you can about angles 1,2,3, and 4

Short Answer

Step by step solution

Step 1. Show that ΔUWX≅ΔVWX.

Step 2. Show that ∠3≅∠4.

Step 3. Show that ∠1≅∠2.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

Given: $\bar{W X} ⊥ \bar{U V}; \bar{W X} ⊥ \bar{Y Z}; \bar{W U} ≅ \bar{W V}$
Prove whatever you can about angles 1,2,3, and 4