   Chapter 3.CT, Problem 1CT ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
1 views

# It is given that Δ A B C ≅ Δ D E F (triangles not shown) a) If m ∠ A = 37 ° and m ∠ E = 68 ° , find m ∠ F .                                     _ b) If A B = 7.3   cm , B C = 4.7   cm , and A C = 6.3   cm ,find E F .                                     _

To determine

a)

To find:

The value of mF.

Solution:

The value of mF is 75°.

Explanation

The measure of sum of angles of a triangle is equal to 180°.

Given:

ΔABCΔDEF, mA=37°

And,

mE=68°

Calculation:

In ΔABC and ΔDEF,

mA=mD=37°

Equate the measure of sum of angles of ΔDEF is equal to 180°.

mD+mE+mF=180°(1)

Substitute 37° for mD and 68° for mE in equation (1) in order to find the value of mF

37°+68°+mF=180°mF=180°37°68°=75°

Conclusion:

Therefore, the value of mF is 75°.

To determine

b)

To find:

The value of EF.

Solution:

The value of EF is 4.7cm.

Explanation

If two triangles are congruent, then all sides of the triangles are congruent.

Given:

ΔABCΔDEF, AB=7.3cm, BC=4.7cm

And,

AC=6.3cm

Calculation:

In ΔABC and ΔDEF,

BC=EF

Substitute 4.7cm for BC in above relation in order to get the value of EF.

4.7cm=EFEF=4.7cm

Conclusion:

Therefore, the value of EF is 4.7cm.

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