Question

1. suppose the two triangles depicted below are similar (pictures are not necessarily to scale). what is the approximate length of x?

triangles: left with base 8, sides x; right with base 12, sides 20
a) 10.0
b) 13.3
c) 16.0
d) 18.8

1. which of the following statements is not true, for a rhombus?

a) the opposite angles of the shape are equal in measure.
b) the shape must have at least one angle measuring 90°.
c) opposite sides of the shape are parallel.
d) the sum of the interior angles is 360°.

Explanation:

Question 15

Step1: Set up proportion for similar triangles

Since the triangles are similar, the ratios of corresponding sides are equal. So, $\frac{x}{20} = \frac{8}{12}$.

Step2: Solve for x

Cross - multiply: $12x = 20\times8$. Then $12x = 160$. Divide both sides by 12: $x=\frac{160}{12}\approx13.3$.

• Option A: In a rhombus, opposite angles are equal. This is true.
• Option B: A rhombus does not have to have a right angle. A rhombus with right angles is a square, but a general rhombus can have non - right angles. So this statement is not true.
• Option C: Opposite sides of a rhombus are parallel (it is a parallelogram). This is true.
• Option D: The sum of interior angles of any quadrilateral (including a rhombus) is $360^{\circ}$. This is true.

Answer:

B) 13.3

Question 16