Question

1. a triangle with side lengths 5, 12, and 13 is dilated to create a similar triangle with side lengths 30, 72, and 78. what is the dilation fact

a. 6
b. \frac{5}{6}
c. 10
d. \frac{1}{6}

1. if triangles acd and xyz are similar by the aa criterion, what can be said about their corresponding sides?

a. they are proportional.
b. they are perpendicular.
c. they are parallel.
d. they are equal.

1. which theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two

a. pythagorean theorem
b. aa criterion
c. sss criterion
d. sas criterion

Explanation:

Question 7

Step1: Recall dilation factor formula

The dilation factor \( k \) is the ratio of the length of a side of the image (dilated triangle) to the corresponding side of the original triangle.

Step2: Calculate the ratio

Take the corresponding sides, e.g., original side \( 5 \) and image side \( 30 \). Then \( k=\frac{30}{5} = 6 \). We can check with other sides: \( \frac{72}{12}=6 \) and \( \frac{78}{13}=6 \).

By the definition of similar triangles (AA criterion means two angles are equal, so triangles are similar), corresponding sides of similar triangles are proportional. Perpendicular, parallel, or equal don't define similar triangle sides.

The Pythagorean Theorem states that in a right - triangle, \( c^{2}=a^{2}+b^{2} \), where \( c \) is the hypotenuse and \( a,b \) are the other two sides. AA, SSS, SAS are criteria for triangle similarity or congruence, not related to this right - triangle side - square relationship.

Answer:

a. 6

Question 8