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Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

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Chapter
Section
BuyFindarrow_forward

Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

In Exercises 13 to 16, provide the missing reasons.

Given: Δ D E T  and  A B C D

Prove: Δ A B E Δ C T B

PROOF
Statements Reasons
1. Δ D E T  and  A B C D 1. ?
2. A B ¯ D T ¯ 2. Opposite sides of a are
3. E B A T 3. ?
4. E D ¯ C B ¯ 4. ?
5. E C B T 5.?
5. Δ A B E Δ C T B 6. ?

To determine

To provide:

The missing reasons.

Explanation

Given:

Given: ΔDET and ABCD

Prove: ΔABEΔCTB

PROOF
Statements Reasons
1. ΔDET and ABCD 1. ?
2. AB¯DT¯ 2. Opposite sides of are
3. EBAT 3. ?
4. ED¯CB¯ 4. ?
5. ECBT
6. ΔABEΔCTB
5. ?
6. ?

Definition:

AA:

If the two angles of one triangle are congruent to the two angles of another triangle, then the triangles are similar.

Description:

Given that ΔDET and ABCD.

To Prove: ΔABEΔCTB

Given AB¯DT¯.

It is known that if two parallel lines AB and DT are cut by a transversal, corresponding angles are congruent.

Therefore, EBAT.

Since opposite sides of a are parallel, ED¯CB¯

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