Chapter 5: Q31 (page 188)

Given: Rectangle $QRST$ ; $▱ RKST$ ; $▱ JQST$
Prove: $\bar{JT} ≅ \bar{KS}$ .

Short Answer

Expert verified

$\bar{JT} ≅ \bar{KS}$

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 $▱ R K S T$ with parallelogram $▱ J Q S T$ .

In parallelogram $▱ R K S T$ , $R T$ and $S K$ are opposite sides which are parallel,

Therefore, $\bar{R T} ≅ \bar{S K}$

Similarly, in parallelogram $▱ J Q S T$ , $J T$ and $Q S$ are opposite sides which are parallel,

Therefore, $\bar{J T} ≅ \bar{Q S}$ .

Now, in rectangle $Q R S T$ , $T R$ and $Q S$ are diagonal of the rectangle and as the diagonal of the rectangle are equal to each other, it can be said that, $\bar{T R} ≅ \bar{Q S}$ .

From the above three relations by the property of transitivity of congruence, $\bar{J T} ≅ \bar{K S}$ .

Hence, $\bar{J T} ≅ \bar{K S}$ .

Step 3. State the conclusion.

Therefore, $\bar{J T} ≅ \bar{K S}$ (proved).

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Given: Rectangle $QRST$ ; $▱ RKST$ ; $▱ JQST$
Prove: $\bar{JT} ≅ \bar{KS}$ .

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

Applied Mathematics

Probability and Statistics

Geometry

Decision Maths

Discrete Mathematics

Pure Maths

Study anywhere. Anytime. Across all devices.

Given: Rectangle QRST; ▱RKST; ▱JQSTProve: JT¯≅KS¯.

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

Applied Mathematics

Probability and Statistics

Geometry

Decision Maths

Discrete Mathematics

Pure Maths

Study anywhere. Anytime. Across all devices.

Given: Rectangle $QRST$ ; $▱ RKST$ ; $▱ JQST$
Prove: $\bar{JT} ≅ \bar{KS}$ .