Question

1. in an animation, a triangle is scaled down by a factor of 2. if the original triangle had sides 10, 14, and 20, what are the side lengths of the scaled triangle?

a. 5,7, and 10
b. 4,6, and 8
c. 5,6, and 10
d. 8,12, and 16

1. if △abc has sides 3,4,5 and △def has sides 9, 12, and 15, are the triangles similar?

a. no
b. yes
c. only if the perimeters are equal
d. only if the angles are equal

1. why is it important to verify proportionality of sides in sas similarity?

a. to measure the perimeter of each triangle
b. to ensure that the scale factor between the triangles is consistent
c. to determine the volume of a shape
d. to confirm that the triangles have equal angles

Explanation:

Step1: Calculate scaled - down side lengths

When a triangle is scaled down by a factor of 2, we divide each original side length by 2. Given original side lengths 10, 14, and 20. New side lengths are $\frac{10}{2}=5$, $\frac{14}{2}=7$, $\frac{20}{2}=10$.

Step2: Check similarity of triangles

For two triangles $\triangle ABC$ with sides 3, 4, 5 and $\triangle DEF$ with sides 9, 12, 15. The ratio of corresponding sides is $\frac{9}{3}=\frac{12}{4}=\frac{15}{5} = 3$. So the triangles are similar.

Step3: Understand the importance of side - proportionality in SAS similarity

In SAS (Side - Angle - Side) similarity, verifying the proportionality of sides ensures that the scale factor between the two triangles is consistent.

Answer:

1. a. 5, 7, and 10
2. b. Yes
3. b. To ensure that the scale factor between the triangles is consistent