Open in App
Log In Start studying!

Select your language

Suggested languages for you:
Deutsch (DE)
Deutsch (UK)
Deutsch (US)

Americas

Europe

Chapter 8: Chapter 8

Problem 121

Next question

Given: $\underline{C A} \cong \underline{D B} \cdot \underline{C B} \cong \underline{D A} .\( Prove \)\triangle A B C \cong \triangle B A D$.

Short Answer

Expert verified
In the given problem, we have \(CA \cong DB\) and \(CB \cong DA\). Since AB is a common side of both triangles, we have \(AB \cong AB\). By the Side-Side-Side (SSS) congruence theorem, we can conclude that \(\triangle ABC \cong \triangle BAD\).
See the step by step solution

Step by step solution

Unlock all solutions

Get unlimited access to millions of textbook solutions with Vaia Premium

Try Premium for free

Over 22 million students worldwide already upgrade their learning with Vaia!

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Identify congruent sides in the triangles

In the given problem, we have the following congruent sides: - Line segment CA is congruent to line segment DB. - Line segment CB is congruent to line segment DA. We can write these congruent relationships as \(CA \cong DB\) and \(CB \cong DA\).

Step 2: Determine the third pair of congruent sides

From the given information, we can conclude that the third pair of congruent sides is AB, which is the common side of both triangles. We can write this as \(AB \cong AB\).

Step 3: Prove the triangles' congruence using SSS theorem

Now that we have all pairs of congruent sides, we can use the SSS congruence theorem to prove that the triangles are congruent. The SSS theorem states that if all three sides of one triangle are congruent to the three corresponding sides of another triangle, then the two triangles are congruent. We have: - \(CA \cong DB\) - \(CB \cong DA\) - \(AB \cong AB\) By the SSS theorem, we can conclude that \(\triangle ABC \cong \triangle BAD\).

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Access millions of textbook solutions in one place

  • Access over 3 million high quality textbook solutions
  • Access our popular flashcard, quiz, mock-exam and notes features
  • Access our smart AI features to upgrade your learning
Get Vaia Premium now
Access millions of textbook solutions in one place

Most popular questions from this chapter

Chapter 8

$\underline{\mathrm{DB}} \cong \underline{\mathrm{EA}}, \underline{\mathrm{AD}} \cong \underline{\mathrm{BE}} .\( Prove: \)\angle \mathrm{DAB} \cong \angle \mathrm{EBA}$
Chapter 8

Prove the median of the base of an isosceles triangle is perpendicular to the base.(In the figure, \(\Delta \mathrm{ABC}\) is isosceles, such that \(\underline{\mathrm{CA}} \cong \underline{\mathrm{CB}}\), and \(\underline{\mathrm{CM}}\) is the median to base \(\underline{\mathrm{AB}}\). Prove \(\underline{C M} \perp \underline{A B}\).)
Chapter 8

Let \(\mathrm{ABC}\) be an equilateral triangle. Let \(\mathrm{D}\) be the midpoint of \(\underline{A B}\). Prove that $\triangle D C B \cong \triangle D C A\(. What kind of triangle is \)\triangle \mathrm{DCB}$ ? What can be said about \(\angle \mathrm{ACD}\) and \(\angle \mathrm{BCD} ?\) (See Figure.)
Chapter 8

Given: \(\mathrm{DC} \cong \mathrm{BA}, \mathrm{AD} \cong \mathrm{CB}\). Prove: \(\triangle \mathrm{ABD} \cong \Delta \mathrm{CDB}\)
Chapter 8

Prove: the median drawn to the base of an isosceles triangle bisects the vertex angle.
See all solutions

More chapters from the book ‘Geometry’

See all chapters

Join over 22 million students in learning with our Vaia App

The first learning app that truly has everything you need to ace your exams in one place.

  • Flashcards & Quizzes
  • AI Study Assistant
  • Smart Note-Taking
  • Mock-Exams
  • Study Planner
Join over 22 million students in learning with our Vaia App
Create your free account now
Join over 22 million students in learning with our Vaia App

Recommended explanations on Math Textbooks

Math

Calculus

Read Explanation
Math

Statistics

Read Explanation
Math

Probability and Statistics

Read Explanation
Math

Decision Maths

Read Explanation
Math

Pure Maths

Read Explanation
Math

Mechanics Maths

Read Explanation
View all explanations