Using Similarity Criteria to Find the Distance Across a Canyon

This lesson teaches how to solve problems using similarity criteria, focusing on the vertical angle theorem and angle-angle similarity postulate. The core lesson involves finding the distance across a canyon using similar triangles. By creating two right triangles and using the properties of similar triangles, the lesson demonstrates how to set up proportions and solve for unknown distances. The calculated distance across the canyon is 218 feet.

What does the vertical angle theorem state about vertical angles?

• They are always complementary.

• They are always right angles.

• They are always supplementary.

• They are always equal.

According to the angle-angle similarity postulate, when are two triangles similar?

• When they have two pairs of congruent angles.

• When they have two pairs of equal sides.

• When they have one pair of congruent angles.

• When they have one pair of equal sides.

What is the first step in finding the distance across the canyon?

• Turn 90 degrees to the right.

• Measure the distance from point W to V.

• Find a landmark across the canyon.

• Walk 600 feet in a straight line.

How far do you walk in a straight line after turning 90 degrees at point Y?

• 200 feet

• 800 feet

• 400 feet

• 600 feet

What is the distance from point W to V?

• 327 feet

• 400 feet

• 600 feet

• 218 feet

What is the simplified ratio of the sides yz to wz in the similar triangles?

• 1/2

• 3/4

• 4/5

• 2/3

What is the calculated distance across the canyon?

• 218 feet

• 400 feet

• 600 feet

• 327 feet