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Chapter 5: Q5 (page 186)

When you know that one angle of a parallelogram is a right angle, you can prove that the parallelogram is a rectangle. Draw a diagram and explain.

Short Answer

Expert verified

The parallelogram is a rectangle.

Step by step solution

01

Step 1. Check the figure.

Draw the figure.

02

Step 2. Step description.

Consider that ∠A=90∘.

Here ABCD is a parallelogram.

Since the opposite sides of a parallelogram are parallel thus, AD∥BC.

As the adjacent angles of a parallelogram are supplementary thus ∠A+∠B=180∘.

Since ∠A=90∘then simplify ∠A+∠B=180∘as follows:

∠A+∠B=180∘90∘+∠B=180∘∠B=180∘−90∘∠B=90∘

03

Step 3. Step description.

Similarly, the opposite sides of a parallelogram are parallel AB∥CD.

∠A+∠D=180∘90∘+∠D=180∘∠D=180∘−90∘∠D=90∘

Again, the opposite sides of a parallelogram are parallel AD∥BC.

∠D+∠C=180∘90∘+∠C=180∘∠C=180∘−90∘∠C=90∘

Thus, ABCD is a parallelogram such that ∠A=∠B=∠C=∠D=90∘.

Therefore, ABCD is a rectangle.

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Most popular questions from this chapter

Must quad. EFGH be a parallelogram? Can it be a parallelogram? Explain.

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

SA¯∥KC¯;role="math" localid="1637731683825" SK¯∥AC¯

Given: ABCD is a ▱,CD¯≅CE¯

Prove: ∠A≅∠E

For the following figure, if OE=4and WE=8, name two segments congruent to WE¯.

The coordinates of three vertices of parallelogram ABCD are given. Plot the points and find the coordinates of the fourth vertex.

A(3,2),B(8,2),C(?,?),D(0,5)
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