Chapter 4: Q2. (page 148)

In Exercises 1-6 you are given a diagram that is marked with given information. Give the reason for each key step of the proof.
Prove: $\bar{BE} ≅ \bar{DF}$
Key steps of proof:
a. width="112" height="20" role="math">ΔABC≅ΔCDA
b. $∠ 1 ≅ ∠ 2$
c. $Δ ABE ≅ Δ CDF$
d. $\bar{BE} ≅ \bar{DF}$

Short Answer

Expert verified

a. $Δ A B C ≅ Δ C D A$	SSS postulate
b. $∠ 1 ≅ ∠ 2$	Corr. parts ofwidth="33" height="20" role="math">≅Δ are $≅$ .
c. $Δ A B E ≅ Δ C D F$	AAS postulate
d. $\bar{B E} ≅ \bar{D F}$	Corr. parts of $≅ Δ$ are $≅$ .

Step by step solution

Step 1. Apply SSS postulate.

Consider $Δ A B C$ and $Δ C D A$ in which $\bar{A B} ≅ \bar{C D}$ , $\bar{B C} ≅ \bar{A D}$ and $\bar{A C} ≅ \bar{A C}$ then by SSS postulate $Δ A B C ≅ Δ C D A$ .

Step 2. Description of step.

As $Δ A B C ≅ Δ C D A$ , by corresponding parts of congruent triangles, $∠ 1 ≅ ∠ 2$ .

Step 3. Apply AAS postulate.

Consider $Δ A B E$ and $Δ C D F$ in which $\bar{A B} ≅ \bar{C D}$ , $∠ A E B ≅ ∠ D F C$ and $∠ 1 ≅ ∠ 2$ then by SAS postulate .

Step 4. Description of step.

As $Δ A B E ≅ Δ C D F$ , by corresponding parts of congruent triangles, width="64">BE¯≅DF¯.

Step 5. Give the reason for each key step of the proof.

a. $Δ A B C ≅ Δ C D A$	SSS postulate
b. $∠ 1 ≅ ∠ 2$	Corr. parts of $≅ Δ$ are $≅$ .
c. $Δ A B E ≅ Δ C D F$	AAS postulate
d. $\bar{B E} ≅ \bar{D F}$	Corr. parts of $≅ Δ$ are $≅$ .

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.

Short Answer

Step by step solution

Step 1. Apply SSS postulate.

Step 2. Description of step.

Step 3. Apply AAS postulate.

Step 4. Description of step.

Step 5. Give the reason for each key step of the proof.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Decision Maths

Discrete Mathematics

Probability and Statistics

Geometry

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In Exercises 1-6 you are given a diagram that is marked with given information. Give the reason for each key step of the proof.Prove:BE¯≅DF¯Key steps of proof:a. width="112" height="20" role="math">ΔABC≅ΔCDAb.∠1≅∠2c.ΔABE≅ΔCDFd.BE¯≅DF¯

Short Answer

Step by step solution

Step 1. Apply SSS postulate.

Step 2. Description of step.

Step 3. Apply AAS postulate.

Step 4. Description of step.

Step 5. Give the reason for each key step of the proof.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Decision Maths

Discrete Mathematics

Probability and Statistics

Geometry

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.