Chapter 5: Q30 (page 188)

Given: Rectangle $QRST$ ; $▱ RKST$ ;
Prove: $Δ QSK$ is isosceles.

Short Answer

Expert verified

$Δ QSK$ is isosceles.

Step by step solution

Step 1. State the concept used.

Diagonals of rectangles are equal and bisect each other.

The opposite sides of a parallelogram are equal.

Step 2. State the proof.

Construct a rectangle $Q R S T$ and parallelogram $▱ R K S T$ .

Now join $Q S$ to form triangle $Δ Q S K$ .

It is to prove that $Δ Q S K$ is isosceles which can be proved by showing any two sides of the triangle are of equal length.

In rectangle $Q R S T$ , $T R$ and $S Q$ are the diagonals of the rectangle.

As the diagonals of the rectangle are of equal length, it can be said that $S Q = R T$ .

Now in the parallelogram $R K S T$ , $R T$ and $S K$ are parallel sides of the parallelogram, and thus $R T = K S$ .

Therefore, $S Q = K S$ .

Thus, in $Δ Q S K$ , two sides are equal $(S Q = K S)$ , so we can say that $Δ Q S K$ is an isosceles triangle.

Step 3. State the conclusion.

Therefore, $Δ Q S K$ is isosceles (proved).

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Given: Rectangle $QRST$ ; $▱ RKST$ ;
Prove: $Δ QSK$ is isosceles.

Short Answer

Step by step solution

Step 1. State the concept used.

Step 2. State the proof.

Step 3. State the conclusion.

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Given: Rectangle QRST; ▱RKST;Prove: ΔQSKis isosceles.

Short Answer

Step by step solution

Step 1. State the concept used.

Step 2. State the proof.

Step 3. State the conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Statistics

Discrete Mathematics

Theoretical and Mathematical Physics

Logic and Functions

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Given: Rectangle $QRST$ ; $▱ RKST$ ;
Prove: $Δ QSK$ is isosceles.