Similar Triangles Applications

State the postulate that proves these triangles are similar.

• SSS

• AA

• SAS

• Not similar

Find side length X.

• 16

• 18

• 2.4

• 15

Find side length X.

• 30

• 25

• 15

• 40

To find the height of a very tall pine tree, you place a mirror on the ground and stand where you can see the top of the pine tree.  How tall is the tree?

• 144 feet

• 72 feet

• 36 feet

Kameron, who is 4.5 ft tall, is outside during recess.  He casts a 9 ft shadow.  If the closest tree to Kameron is 18 ft tall, how long is the tree’s shadow?

• 36 ft

• 9 ft

• 27 ft

• 32 ft

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

What does AA similarity theorem state?

• If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

• If two angles of one triangle are congruent to two sides of another triangle, then the triangles are similar.

• If two sides of one triangle are congruent to two sides of another triangle, then the triangles are similar.

• If two sides of one triangle are congruent to two angles of another triangle, then the triangles are similar.

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.

What is the significance of the AA similarity theorem in geometry?

• The AA similarity theorem is used to calculate the area of a triangle

• The AA similarity theorem is only applicable to right-angled triangles

• The AA similarity theorem is used to find the sum of the angles in a triangle

• The significance of the AA similarity theorem is that it provides a quick and easy way to determine if two triangles are similar without having to measure all their sides.

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.