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Chapter 5: Q31 (page 170)

Given: ABCD is a ▱,CD¯≅CE¯

Prove: ∠A≅∠E

Short Answer

Expert verified

It is proved that ∠A≅∠E.

Step by step solution

01

Step 1. Apply properties of parallelogram.

Opposite angles of a parallelogram are congruent.

In ▱ABCD, ∠Aand ∠BCDare opposite angles. Therefore, ∠A≅∠BCD.

02

Step 2. Description of step.

From the given figure, it can be observed that BC¯∥AD¯and CD¯is a transversal then ∠BCDand ∠CDEare alternate interior angles such that, ∠BCD≅∠CDE.

03

Step 3. Isosceles triangle theorem.

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

Consider ΔCDE, in which CD¯≅CE¯then by isosceles triangle theorem, ∠CDE≅∠E

04

Step 4. Description of step.

As ∠A≅∠BCD, ∠BCD≅∠CDEand ∠CDE≅∠Ethen by the transitive property of congruence ∠A≅∠E.

Hence it is proved that ∠A≅∠E.

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Most popular questions from this chapter

In Exercises 5-10 quad. PQRS is a parallelogram. Find the values of a, b, x and y.

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

Theorem 5-7.

Draw a quadrilateral that has two pairs of congruent sides but that is not a parallelogram.

Quadrilateral is a parallelogram.

  1. Why is supplementary to ?
  2. Why is supplementary to ?
  3. Complete: consecutive angles of a parallelogram are ?, while opposite angles are?.

Quadrilateral ABCD is a parallelogram. Name the principal theorem or definition that justifies the statement.

DX=BX
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