Question

!50 POINTS! (3 SIMPLE GEOMETRY QUESTIONS)

QUESTIONS BELOW
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Answer 1

1) a) HJG

2) c) x=11, y = 27.6

3) b) A, B and C are collinear

Explanation:

1) a) HJG

∠FJI = ∠HJG

FJ ≅ HJ

JI ≅ JG

2) 3x - 9 = 24

⇒ 3x = 24+9

⇒ 3x = 33

⇒ x = 33/3

⇒ x = 11

3y = 82.8

⇒ y = 82.8/3

⇒ y = 27.6

Chk:

1.5y = 41.4

⇒ y = 41.4/1.5

⇒ y = 27.6

3) Since A B amd C are collinear and the angles opposite to the collinear line is the same, the two triangles are similar

Answer 2

1 a HJG

2 c x = 11; y = 27.6

3 a

Explanation:

1.

Angles FJI and GJH are congruent because they are vertical. From here, you have vertex J corresponding to vertex J.

Angles F and H are congruent because they are alternate interior angles of parallel lines. From here you have vertex F corresponding to vertex H.

The given triangle is triangle FJI.

We know that FJ correspond to HJ, so triangle FJI is congruent to triangle HJG.

Answer: a HJG

2.

Sides MN and PR are corresponding sides, so they are congruent.

3x - 9 = 24

3x = 33

x = 11

Angles O and T are corresponding and congruent angles.

3y = 82.8°

y = 27.6°

Answer: c x = 11; y = 27.6

3.

Let's look at each case and explain it.

a

Angles D and C are congruent.

The vertical angles are congruent.

By AA Similarity, the triangles are congruent.

b

We have 2 triangles, and all we know is one angle of one triangle is congruent to one angle of the other triangle. That is not enough to prove that the triangles are similar.

c

We have one pair of congruent angles and one side common to both triangles. That is not enough to prove similar triangles.

d

We have one pair of congruent angles and one side common to both triangles. That is not enough to prove similar triangles.