Chapter 4: Q4. (page 129)

Describe your plan for proving the following.
Given: $\bar{Z W} ∥ \bar{Y X}; \bar{Z W} ≅ \bar{X Y}$ Prove: $\bar{Z Y} ∥ \bar{W X}$

Short Answer

Expert verified

$\bar{Z X} ≅ \bar{Z X}$ (reflexive property)

$∠ 3 ≅ ∠ 4$ (alternate interior angles are equal)

$Δ W Z X ≅ Δ Y X Z$ (SAS congruence criteria)

$∠ 1 ≅ ∠ 2$ (corresponding parts of congruent triangles)

$\bar{Z Y} ∥ \bar{W X}$ (as alternate interior angles are equal)

Step by step solution

Step 1. Show ZX¯≅XZ¯.

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

Step 2. Show ∠3≅∠4.

if two lines are parallel then the alternate interior angles are equal.

Step 3. Show ΔWZX≅ΔYXZ.

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

So, from step 1, step 2 and given

$Δ W Z X ≅ Δ Y X Z$

Step 4. Show ∠1≅∠2.

As corresponding parts of congruent triangles are equal

So, $∠ 1 ≅ ∠ 2$

Step 5. Show ZY¯∥WX¯.

As alternate interior angles are equal then lines are parallel

Thus, $\bar{Z Y} ∥ \bar{W X}$

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Describe your plan for proving the following.
Given: $\bar{Z W} ∥ \bar{Y X}; \bar{Z W} ≅ \bar{X Y}$ Prove: $\bar{Z Y} ∥ \bar{W X}$

Short Answer

Step by step solution

Step 1. Show ZX¯≅XZ¯.

Step 2. Show ∠3≅∠4.

Step 3. Show ΔWZX≅ΔYXZ.

Step 4. Show ∠1≅∠2.

Step 5. Show ZY¯∥WX¯.

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Describe your plan for proving the following.Given:ZW¯∥YX¯;ZW¯≅XY¯ Prove:ZY¯∥WX¯

Short Answer

Step by step solution

Step 1. Show ZX¯≅XZ¯.

Step 2. Show ∠3≅∠4.

Step 3. Show ΔWZX≅ΔYXZ.

Step 4. Show ∠1≅∠2.

Step 5. Show ZY¯∥WX¯.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Pure Maths

Probability and Statistics

Theoretical and Mathematical Physics

Calculus

Logic and Functions

Study anywhere. Anytime. Across all devices.

Describe your plan for proving the following.
Given: $\bar{Z W} ∥ \bar{Y X}; \bar{Z W} ≅ \bar{X Y}$ Prove: $\bar{Z Y} ∥ \bar{W X}$