Question

!50 POINTS! (3 SIMPLE GEOMETRY QUESTIONS)

QUESTIONS BELOW
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Answer 1

1st one: a. AA

2nd one: a. SAS

3rd one :
`\tt blank\: \boxed{\tt (2)/(3)}`

Explanation:

Note:

Properties of similar triangles:

• The Side-Angle-Side Similarity Axiom (SAS). This axiom states that if two triangles have two pairs of corresponding sides that are in proportion and the included angles are congruent, then the triangles are similar.
• The Side-Side-Side Similarity Axiom (SSS). This axiom states that if two triangles have three pairs of corresponding sides that are in proportion, then the triangles are similar.

• The Angle-Angle Similarity Axiom (AA). This axiom states that if two triangles have two pairs of corresponding angles that are congruent, then the triangles are similar.

For 1st Question:

In Δ XYZ and ΔUPG

∡X=∡U = 180°-144°-10°=26°

∡Z=∡G = 144°

∡Y=∡P= 26°

Since triangles will be similar when it fulfills the Angle-Angle Similarity Axiom (AA).

Therefore, answer is a. AA

`\hrulefill`

For Second question:

In Δ XYZ and ΔRTA

∡X=∡U

`\tt (XY)/(RT)=(4)/(6)=(2)/(3)`

`\tt (XZ)/(RA)=(3)/(4.5)=(2)/(3)`

Since triangles will be similar when it fulfills the the Side-Angle-Side Similarity Axiom (SAS).

Therefore, answer is a. SAS

`\hrulefill`

For third question:

let's take the scale factor of smaller triangle to bigger triangle:

Scale factor means the ratio of the sides of the similar triangle.

Since Δ XYZ and ΔRTA are similar.

Ratio of their side

`\tt (XY)/(RT)=(4)/(6)=(2)/(3)`

`\tt (XZ)/(RA)=(3)/(4.5)=(2)/(3)`

We got the same ratio.

So, the scale factor is
`(2)/(3)`