Question

!50 POINTS! (3 SIMPLE GEOMETRY QUESTIONS)

QUESTIONS BELOW
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Answer 1

1st answer: a.(2,1)

2nd answer: b. 9 ft, 12 ft, 15 ft

3rd answer: a.

Explanation:

For 1st Question;

To make a congruent triangle, it must fulfill ASA, SSS, SAS,etc. axiom.

When we plot D(2,1) we get,

AB=DC=4.1

BC=AD= 4

AC= AC
Since, ABC≅ACD by SSS axiom.

For more detail: See attachment

Therefore, answer is a.(2,1)

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For 2nd Question:

To make a similar triangle the corresponding side should be proportional.

let's check a.

3/8=3/8

4/11=4/11

Since the side are not proportional so they are not similar triangle.

Let's check b.

3/9=1/3

4/12=1/3

5/15=1/3

Since the side are proportional so they are similar triangle.

Therefore, the answer is b. 9 ft, 12 ft, 15 ft

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For 3rd Question:

To make a similar triangle the corresponding angle should be equal.

let's check a.

∡D=∡C Given

They are equal means that AD ║ BC.

∡A=∡B alternate interior angle

And remaining angle will be automatically equal as a remaining angle of a triangle. By AA postulate

So, option a. contains a pair of similar triangle,