Chapter 5: Q32 (page 170)

Given: ABCDis a $▱, ∠ A ≅ ∠ E$
Prove: localid="1637661691185" $\bar{A B} ≅ \bar{C E}$

Short Answer

Expert verified

It is proved that $\bar{A B} ≅ \bar{C E}$ .

Step by step solution

Step 1. Apply property of parallelogram.

The opposite sides of a parallelogram are congruent.

In $▱ A B C D$ , $\bar{A B}$ and $\bar{C D}$ are opposite sides. Therefore, $\bar{A B} ≅ \bar{C D}$ .

Step 2. Description of step.

From the given figure, it can be observed that $\bar{B C} ∥ \bar{A D}$ and $\bar{A D}$ is a transversal then $∠ A$ and $∠ C D E$ are corresponding angles such that, $∠ A ≅ ∠ C D E$ .

Step 3. Description of step.

It is given that, $∠ A ≅ ∠ E$ and from step 2, $∠ A ≅ ∠ C D E$ then by the transitive property of congruence, $∠ C D E ≅ ∠ E$ .

Step 4. Converse of isosceles triangle theorem.

If two angles of a triangle are congruent then the sides opposite to those angles are congruent.

Consider $Δ C D E$ , in which $∠ C D E ≅ ∠ E$ then by the converse of isosceles triangle theorem, $\bar{C D} ≅ \bar{C E}$ .

Step 5. Description of step.

As $\bar{A B} ≅ \bar{C D}$ and $\bar{C D} ≅ \bar{C E}$ then by the transitive property of congruence, $\bar{A B} ≅ \bar{C E}$ .

Hence it is proved that $\bar{A B} ≅ \bar{C E}$ .

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Given: ABCDis a $▱, ∠ A ≅ ∠ E$
Prove: localid="1637661691185" $\bar{A B} ≅ \bar{C E}$

Short Answer

Step by step solution

Step 1. Apply property of parallelogram.

Step 2. Description of step.

Step 3. Description of step.

Step 4. Converse of isosceles triangle theorem.

Step 5. Description of step.

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Given: ABCDis a ▱,∠A≅∠EProve: localid="1637661691185" AB¯≅CE¯

Short Answer

Step by step solution

Step 1. Apply property of parallelogram.

Step 2. Description of step.

Step 3. Description of step.

Step 4. Converse of isosceles triangle theorem.

Step 5. Description of step.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Logic and Functions

Probability and Statistics

Statistics

Decision Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Given: ABCDis a $▱, ∠ A ≅ ∠ E$
Prove: localid="1637661691185" $\bar{A B} ≅ \bar{C E}$