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Geometry

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

$Math Studyset Vaia Explanations$ Math

Student Edition · 227 pages

ISBN: 9780395977279

Chapter 5: Q. 19 (page 201)

Given: $ABCD$ is a parallelogram; $\bar{AD} ≅ \bar{AC}$ ; $\bar{AE} ≅ \bar{EC}$ ; $∠ ADF ≅ ∠ CDF$ ; $m ∠ DAC = 36$ .
Complete each statement about the diagram.
19. $∠ ADF ≅ ∠ CDF$ , so $\bar{DF}$ is a(n) of $∠ ADC$ .

Short Answer

Expert verified

$∠ A D F ≅ ∠ C D F$ , so $\bar{D F}$ is an angle bisector of $∠ A D C$ .

Step by step solution

01

- Observe the given diagram.

The given diagram is:

02

- Write the definition of angle bisector.

The angle bisector is a ray which divides the given angle into two equal angles.

03

- Write the complete statement.

$∠ A D F ≅ ∠ C D F$ , so $\bar{D F}$ is an angle bisector of $∠ A D C$ .

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Most popular questions from this chapter

$▱ DECK$ is a parallelogram. Complete.

If $DE = x + y, EC = 12, CK = 2 x - y$ and $KD = 3 x - 2 y$ then and $x = ?$ , $y = ?$ , and the perimeter of $▱ DECK$

State the principal definition or theorem that enables you to deduce, from the information given, that quadrilateral SACK is a parallelogram.

$S O = \frac{1}{2} S C; K O = \frac{1}{2} K A$

Quadrilateral ABCD is a parallelogram. Name the principal theorem or definition that justifies the statement.

$\bar{A D} ≅ \bar{B C}$

Quadrilateral ABCD is a parallelogram. Name the principal theorem or definition that justifies the statement.

$m ∠ ABC = m ∠ CDA$

For exercises, 14-18 write paragraph proofs.

Given: parallelogram ABCD, $\bar{AN}$ bisects $∠ DAB$ ; $\bar{CM}$ bisects $∠ BCD$ .

Prove: AMCN is a parallelogram.

See all solutions

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