Applications of Similar Triangles

Use the information in the diagram to determine the height of the tree.

• 80 feet

• 320 feet

• 40 feet

• 160 feet

What is the ratio of the side lengths?

• 2.5

• 1.5

• 2

• 1.25

Q1. What is the sum of 105 and 100?

• 205

• 105

• 230

• 135

What are the practical applications of the AA similarity theorem?

• Calculating the area of a circle

• Solving equations in algebra

• The practical applications of the AA similarity theorem include solving problems in geometry, such as determining the similarity of two triangles and finding unknown side lengths or angles.

• Determining the boiling point of a substance

If two angles of one triangle are congruent to two angles of another triangle, then what can be said about the two triangles?

• The two triangles are parallel.

• The two triangles are similar.

• The two triangles are congruent.

• The two triangles are perpendicular.

Can you provide an example of how the AA similarity theorem is used to solve a problem?

• Using the Pythagorean theorem to find the measures of the corresponding sides

• Applying the Law of Sines to determine the unknown angles

• Using the AA similarity theorem to find the area of the triangles

• Identifying congruent angles in two triangles and using the proportionality of corresponding sides to solve for unknown measures.

What are the conditions for the AA similarity theorem to be applicable?

• The triangles have equal side lengths

• The triangles have a common vertex

• The triangles are both equilateral

• Two angles of one triangle are congruent to two angles of another triangle.

How can the AA similarity theorem be used to prove two triangles similar?

• By proving that the two triangles have the same area

• We can use the AA similarity theorem to prove two triangles similar by showing that two angles of one triangle are congruent to two angles of the other triangle.

• By demonstrating that the two triangles have the same perimeter

• By showing that two sides of one triangle are congruent to two sides of the other triangle

In similar figures, what is the relationship between corresponding sides?

• They are parallel

• They are in the same proportion.

• They are equal in length

• They are perpendicular

Which angle corresponds with ∠X?

• ∠N

• ∠W

• ∠E

• ∠Y