Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 227 pages

ISBN: 9780395977279

Chapter 5: Q32 (page 170)

Given: ABCDis a $鈻�, 鈭� A 鈮� 鈭� E$
Prove: localid="1637661691185" $\overset{炉}{A B} 鈮� \overset{炉}{C E}$

Short Answer

Expert verified

It is proved that $\overset{炉}{A B} 鈮� \overset{炉}{C E}$ .

Step by step solution

Step 1. Apply property of parallelogram.

The opposite sides of a parallelogram are congruent.

In $鈻� A B C D$ , $\overset{炉}{A B}$ and $\overset{炉}{C D}$ are opposite sides. Therefore, $\overset{炉}{A B} 鈮� \overset{炉}{C D}$ .

Step 2. Description of step.

From the given figure, it can be observed that $\overset{炉}{B C} 鈭� \overset{炉}{A D}$ and $\overset{炉}{A D}$ is a transversal then $鈭� A$ and $鈭� C D E$ are corresponding angles such that, $鈭� A 鈮� 鈭� C D E$ .

Step 3. Description of step.

It is given that, $鈭� A 鈮� 鈭� E$ and from step 2, $鈭� A 鈮� 鈭� C D E$ then by the transitive property of congruence, $鈭� C D E 鈮� 鈭� E$ .

Step 4. Converse of isosceles triangle theorem.

If two angles of a triangle are congruent then the sides opposite to those angles are congruent.

Consider $螖 C D E$ , in which $鈭� C D E 鈮� 鈭� E$ then by the converse of isosceles triangle theorem, $\overset{炉}{C D} 鈮� \overset{炉}{C E}$ .

Step 5. Description of step.

As $\overset{炉}{A B} 鈮� \overset{炉}{C D}$ and $\overset{炉}{C D} 鈮� \overset{炉}{C E}$ then by the transitive property of congruence, $\overset{炉}{A B} 鈮� \overset{炉}{C E}$ .

Hence it is proved that $\overset{炉}{A B} 鈮� \overset{炉}{C E}$ .

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91影视

Given: ABCDis a $鈻�, 鈭� A 鈮� 鈭� E$
Prove: localid="1637661691185" $\overset{炉}{A B} 鈮� \overset{炉}{C E}$

Short Answer

Step by step solution

Step 1. Apply property of parallelogram.

Step 2. Description of step.

Step 3. Description of step.

Step 4. Converse of isosceles triangle theorem.

Step 5. Description of step.

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91影视

Given: ABCDis a 鈻�,鈭�A鈮�鈭�EProve: localid="1637661691185" AB炉鈮�CE炉

Short Answer

Step by step solution

Step 1. Apply property of parallelogram.

Step 2. Description of step.

Step 3. Description of step.

Step 4. Converse of isosceles triangle theorem.

Step 5. Description of step.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Decision Maths

Pure Maths

Probability and Statistics

Applied Mathematics

Geometry

Study anywhere. Anytime. Across all devices.

Given: ABCDis a $鈻�, 鈭� A 鈮� 鈭� E$
Prove: localid="1637661691185" $\overset{炉}{A B} 鈮� \overset{炉}{C E}$