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Marina86 [1]
3 years ago
12

Figure ABCD is a parallelogram.

Mathematics
2 answers:
Sonbull [250]3 years ago
7 0
Answer is

A. First prove ABC is congruent to CDA, and then state AD and BC are corresponding sides of the triangles.

hope it helps
lutik1710 [3]3 years ago
5 0

Answer:

Option A is correct.

First prove ABC is congruent to CDA and then state AD and BC are corresponding sides of the triangles.

Step-by-step explanation:

Given the figure: ABCD is a parallelogram.

Parallelogram states that the opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

therefore, AB is parallel to CD    [by definition of parallelogram]

here, in the figure, AC becomes a transversal line.

let \triangle CDA and \triangle ABC

Alternate angle property states that the two angles are on opposite sides of the sloping transversal line.

\angle DAC = \angle BCA  [Angle]     [By property of alternate angle]

AC = AC       [Common side]

\angle ACD = \angle BAC  [Angle]       [By property of alternate angle]

ASA (Angle-Side-Angle) Postulates states that if two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.

therefore, by ASA postulates;

\triangle CDA \cong \triangle ABC

Then, by CPCT [ Corresponding part of the congruent triangle]

AD = BC         hence proved!

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In the diagram shown, AE 1/3AC and ED ll CB. Explain why df must be one-fourth length of CD
Blizzard [7]

The value of the length DF is 1/4 of that of CD because of the Angle Bisector Theorem for triangles.

<h3>What is the Angle Bisector Theorem?</h3>

The Angel Bisector Theorem states that if a ray bisects an angle of a triangle, it dissects the side of the triangle that is opposite to the dissected angle into parts that are proportionate to the adjacent sides.

Note that the angle that has been dissected here is ∠CBD. Thus,

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See the link below for more about Angle Bisector Theorem of the Triangle:

brainly.com/question/21475560

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1 year ago
ASAP MAJOR HELP NEEDED. I really need help. I am very confused on how to do this please help.
alexandr402 [8]

Because the 2 sides of the triangle are the same, they are both 21, the two bottom angles would also be the same.


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