Chapter 4: Q11. (page 116)

Suppose you know that $\bar{D B} ⊥ \bar{D C} .$ Explain how you can deduce that $\bar{D B} ⊥ \bar{B A} .$

Short Answer

Expert verified

With the help of the congruency of $Δ A O B ≅ Δ C O D,$ $\bar{D B} ⊥ \bar{B A}$ can be explained.

Step by step solution

Step 1. Define concept of congruent triangles

The two triangles are said to be congruent if they are copies of each other and if their vertices are superposed, then can say that the corresponding angles and the sides of the triangles are congruent.

Step 2. Observe the figure

The two triangles shown in the figure are congruent.

Therefore, if their vertices are superposed, then $Δ A O B ≅ Δ C O D$ is obtained.

Step 3. Deduce DB perpendicular BA

Since $Δ A O B ≅ Δ C O D,$ therefore, $∠ D ≅ ∠ B$ because corresponding parts of congruent triangles are congruent.

Now it is given that $\bar{D B} ⊥ \bar{D C}$ , then $m ∠ D = 90 °$ , and so $\bar{D B} ⊥ \bar{B A}$ , which implies.

Therefore, with the help of the congruency of $Δ A O B ≅ Δ C O D$ , $\bar{D B} ⊥ \bar{B A}$ can be explained.

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.

Suppose you know that $\bar{D B} ⊥ \bar{D C} .$ Explain how you can deduce that $\bar{D B} ⊥ \bar{B A} .$

Short Answer

Step by step solution

Step 1. Define concept of congruent triangles

Step 2. Observe the figure

Step 3. Deduce DB perpendicular BA

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Statistics

Applied Mathematics

Decision Maths

Logic and Functions

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Suppose you know that DB¯⊥DC¯.Explain how you can deduce that DB¯⊥BA¯.

Short Answer

Step by step solution

Step 1. Define concept of congruent triangles

Step 2. Observe the figure

Step 3. Deduce DB perpendicular BA

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Statistics

Applied Mathematics

Decision Maths

Logic and Functions

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Suppose you know that $\bar{D B} ⊥ \bar{D C} .$ Explain how you can deduce that $\bar{D B} ⊥ \bar{B A} .$