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AnnZ [28]
3 years ago
9

Pleas help will give brainlist!

Mathematics
1 answer:
Stolb23 [73]3 years ago
3 0

Answer:

The correct option is;

An isosceles trapezoid with legs of length 8

Step-by-step explanation:

The correct option is an isosceles trapezoid with legs of length 8

The given properties of the quadrilateral are;

1) One pair of equal opposite sides

2) One pair of parallel opposite sides

From the given options, the two options which are not parallelograms are the kite and the trapezoid

However given that the option of the kite has a pair of adjacent side of length 8, with the given pair of equal length opposite side of length 8, we have that all the sides of the quadrilateral will be of length 8, and the figure cannot be a kite

An isosceles trapezoid of leg length 8 has one pair of equal length opposite sides of length 8 and one pair of parallel sides of unequal length

Given that the length of the lines that make up the pair of opposite parallel sides in the figure are not specified, the figure can be described by as being an isosceles trapezoid.

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Answer:

Given: In triangle ABC and triangle DBE where DE is parallel to AC.

In ΔABC and ΔDBE

DE || AC   [Given]

As we know, a line that cuts across two or more parallel lines.  In the given figure, the line AB is a transversal.

Line segment  AB is transversal that intersects two parallel lines.  [Conclusion from statement 1.]

Corresponding angles theorem: two parallel lines are cut by a transversal, then the  corresponding angles are congruent.

then;

\angle BDE \cong \angle BAC  and

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Reflexive property of equality states that if angles in geometric figures can be congruent to themselves.

by Reflexive property of equality:

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therefore, by AAA similarity postulates theorem

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then, we have;

\frac{BD}{BA}                  [By definition of similar triangles]

therefore, the missing statement and the reasons are

Statement                                                                   Reason

3.\angle BDE \cong \angle BAC      Corresponding angles theorem

and  \angle BEC \cong \angle BCA        

5. \triangle ABC \sim \triangle DBE   AAA similarity postulates    

6. BD over BA                                                    Definition of similar triangle



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Answer:

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3 years ago
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