Right Triangle Similarity Theorem

What is the right triangle similarity theorem?

• The right triangle similarity theorem states that all right triangles are congruent

• The right triangle similarity theorem states that if a right triangle is placed inside another right triangle, then the two triangles are similar if the hypotenuse and one other side of the smaller triangle are proportional to the corresponding sides of the larger triangle.

• The right triangle similarity theorem states that the hypotenuse of a right triangle is always equal to the sum of the other two sides

• The right triangle similarity theorem states that the angles of a right triangle are always equal

State the conditions for two right triangles to be similar.

• They have the same hypotenuse length

• They have the same area

• They have the same perimeter

• The conditions for two right triangles to be similar are that their corresponding angles are congruent.

If two right triangles are similar, what can you say about their corresponding angles?

• Corresponding angles of similar right triangles are always acute.

• Corresponding angles of similar right triangles are equal to 90 degrees.

• Corresponding angles of similar right triangles are congruent.

• Corresponding angles of similar right triangles are supplementary.

If two right triangles are similar, what can you say about their corresponding sides?

• The corresponding sides of similar right triangles are in proportion to each other.

• The corresponding sides of similar right triangles are equal in length.

• The corresponding sides of similar right triangles are perpendicular to each other.

• The corresponding sides of similar right triangles are parallel to each other.

Explain the concept of the altitude drawn to the hypotenuse of a right triangle.

• The altitude drawn to the hypotenuse of a right triangle is parallel to the hypotenuse.

• The altitude drawn to the hypotenuse of a right triangle is always equal to the length of the hypotenuse.

• The altitude drawn to the hypotenuse of a right triangle is also known as the median of the triangle.

• The altitude drawn to the hypotenuse of a right triangle divides the hypotenuse into two segments, and the length of each segment is the geometric mean of the lengths of the adjacent sides of the right triangle.

How can you use the right triangle similarity theorem to solve for unknown side lengths?

• Apply the Law of Sines to determine the unknown side lengths

• Calculate the area of the triangle to solve for the unknown side lengths

• Set up a proportion with the known side lengths and the unknown side lengths, then solve for the unknown side length using cross multiplication.

• Use the Pythagorean theorem to find the unknown side lengths

In a right triangle ABC, if angle A is 30 degrees and angle B is 60 degrees, what can you say about the measures of the sides opposite to these angles?

• The side opposite angle A is the longest side, and the side opposite angle B is the shortest side.

• The side opposite angle A is the longest side, and the side opposite angle B is the shortest side.

• The side opposite angle A is the same length as the side opposite angle B.

• The side opposite angle A is the shortest side, and the side opposite angle B is the longest side.

In a right triangle XYZ, if the length of side XY is 6 cm and the length of side YZ is 8 cm, what is the length of side XZ?

• 10 cm

• 12 cm

• 5 cm

• 14 cm

If two right triangles have the same acute angle measures, are they necessarily similar? Explain your answer.

• No, they could have different area

• Yes

• No, they could have different hypotenuse lengths

• No, they could have different side lengths

In a right triangle PQR, if angle P is 45 degrees and angle Q is 45 degrees, what can you say about the measures of the sides opposite to these angles?

• The measures of the sides opposite to angles P and Q are not equal in length.

• The measure of the side opposite to angle P is greater than the measure of the side opposite to angle Q.

• The measure of the side opposite to angle P is less than the measure of the side opposite to angle Q.

• The measures of the sides opposite to angles P and Q are equal in length.