Chapter 5: Q. 18 (page 199)

For the following figure, given that $▱ P Q R S; P A = R B$ then prove that $A S = B Q$ .

Short Answer

Expert verified

Thus, the statement is $A S = B Q$ .

Step by step solution

Step 1- Check the figure.

Consider the figure.

Step 2- Apply the SAS postulate.

SAS postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the triangles are congruent.

Step 3- Step description.

Consider the triangles $P A S$ and $R B Q$ .

Consider $P A = R B$ .

Use the definition of parallelogram such that

$\begin{array}{l} P S = R Q \\ ∠ P = ∠ R \end{array}$

Use the SAS postulate that implies that $Δ P A S ≅ Δ R B Q$ .

As the corresponding parts of congruent triangles are congruent thus the sides are congruent such that $A S = B Q$ .

Therefore $A S = B Q$ .

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For the following figure, given that $▱ P Q R S; P A = R B$ then prove that $A S = B Q$ .

Short Answer

Step by step solution

Step 1- Check the figure.

Step 2- Apply the SAS postulate.

Step 3- Step description.

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For the following figure, given that ▱PQRS;PA=RBthen prove thatAS=BQ .

Short Answer

Step by step solution

Step 1- Check the figure.

Step 2- Apply the SAS postulate.

Step 3- Step description.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Applied Mathematics

Decision Maths

Theoretical and Mathematical Physics

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Mechanics Maths

Study anywhere. Anytime. Across all devices.

For the following figure, given that $▱ P Q R S; P A = R B$ then prove that $A S = B Q$ .