Chapter 5: Q29 (page 170)

Given: $▱ PQRS;$ localid="1637659881844" $\bar{P J} ≅ \bar{R K}$
Prove: localid="1637659923835" $\bar{S J} ≅ \bar{Q K}$

Short Answer

Expert verified

It is proved that $\bar{S J} ≅ \bar{Q K}$ .

Step by step solution

Step 1. Apply property of parallelogram.

The opposite sides of a parallelogram are congruent.

From the given figure, it can be observed that $\bar{S P}$ and $\bar{R Q}$ are opposite sides of a $▱ P Q R S$ .

Therefore, $\bar{S P} ≅ \bar{R Q}$

Step 2. Apply property of parallelogram.

The opposite angles of a parallelogram are congruent.

From the given figure, it can be observed that $∠ P$ and $∠ R$ are opposite angles of a $▱ P Q R S$ .

Therefore, $∠ P ≅ ∠ R$ .

Step 3. Apply SAS postulate.

If two sides and the included angle of one triangle are congruent to two sides and included angle of another triangle, then the triangles are congruent.

Here, $\bar{P J} ≅ \bar{R K}$ , $∠ P ≅ ∠ R$ and $\bar{S P} ≅ \bar{R Q}$ , then by SAS postulate $Δ S P J ≅ Δ K R Q$ .

Step 4. Description of step.

As $Δ S P J ≅ Δ K R Q$ , then by corresponding parts of congruent triangles, $\bar{S J} ≅ \bar{Q K}$ .

Hence it is proved that $\bar{S J} ≅ \bar{Q K}$ .

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Given: $▱ PQRS;$ localid="1637659881844" $\bar{P J} ≅ \bar{R K}$
Prove: localid="1637659923835" $\bar{S J} ≅ \bar{Q K}$

Short Answer

Step by step solution

Step 1. Apply property of parallelogram.

Step 2. Apply property of parallelogram.

Step 3. Apply SAS postulate.

Step 4. Description of step.

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Given:▱PQRS;localid="1637659881844" PJ¯≅RK¯Prove: localid="1637659923835" SJ¯≅QK¯

Short Answer

Step by step solution

Step 1. Apply property of parallelogram.

Step 2. Apply property of parallelogram.

Step 3. Apply SAS postulate.

Step 4. Description of step.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Probability and Statistics

Discrete Mathematics

Logic and Functions

Pure Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Given: $▱ PQRS;$ localid="1637659881844" $\bar{P J} ≅ \bar{R K}$
Prove: localid="1637659923835" $\bar{S J} ≅ \bar{Q K}$