Similar Triangle Multiple Parallel Lines

Triangle CAT and triangle DOG are similar triangles. What is the measure of ∠T?

• 55°

• 57°

• 68°

• 123°

Triangle QRS is similar to triangle TUV. Angle R is congruent to angle U. Angle S is congruent to angle V. Based on the diagram, what is the measure of angle Q?

• Angle Q measures 17° because angle R measures 63 and 80 - 63 = 17.

• Angle Q measures 50° because 180 - 80 = 100 and 100 ÷ 2 = 50.

• Angle Q measures 37° because angle R measures 63 and 180 - (63 + 80) = 37.

• There is not enough information to determine the measure of angle Q.

In the diagram, triangle ABC and triangle XYZ are both right triangles. ∠A is congruent to ∠X. Which statement about the triangles must be true?

• The measure of ∠B is less than the measure of ∠Y because triangle ABC is smaller than triangle XYZ.

• The measure of ∠B is the same as the measure of ∠Y because triangle ABC and triangle XYZ are similar.

• The measure of ∠B is the same as the measure of ∠Y because triangle ABC and triangle XYZ are congruent.

• The measure of ∠B is greater than the measure of ∠Y because triangle ABC and triangle XYZ are similar.

If two triangles are similar, how does that relate to their slopes?

• The slopes of corresponding sides are unrelated.

• The slopes of corresponding sides of similar triangles are proportional.

• The slopes of corresponding sides are always equal.

• The slopes of similar triangles are always negative.

Is ABC ~ DEC? Explain.

• No; They are both right triangles but all of their sides are different, so they are not similar.

• Yes; They share two sides, so they are similar.

• Yes; They are both right triangles and they share the common angle C, so they are similar.

• There is not enough information to tell whether they are similar.

How can you use similar triangles to find the slope of a line?

• The slope can be calculated using the area of the triangle formed by the line.

• The slope of a line can be found using the formula m = (y2 - y1) / (x2 - x1) based on the rise over run from similar triangles.

• You can find the slope by measuring the angles of the triangles.

• The slope is determined by the length of the hypotenuse of the triangle.

Solve for X

• 96

• 84

• 62

• 34

Solve for x

• 85

• 90

• 100

• 105

Solve for x

• 52

• 46

• 82

• 72

Solve for x

• 40

• 50

• 60

• 80