Exploring Triangle Similarities: AA Criterion & Angles

In triangle ABC, angle A is 40 degrees and angle B is 60 degrees. Prove that triangle ABC is similar to triangle DEF, where angle D is 40 degrees. What is angle E?

• 60 degrees

• 70 degrees

• 50 degrees

• 80 degrees

A tree casts a shadow of 15 feet. At the same time, a 6-foot tall person casts a shadow of 4 feet. Are the triangles formed by the tree and its shadow similar to the triangles formed by the person and their shadow?

• Yes, the triangles are similar.

• The triangles are similar only if the tree is taller.

• The triangles are similar only if the shadows are equal in length.

• No, the triangles are not similar.

In triangle GHI, angle G is 50 degrees and angle H is 30 degrees. If triangle JKL is similar to triangle GHI and angle J is 50 degrees, what is angle K?

• 60 degrees

• 80 degrees

• 90 degrees

• 100 degrees

A ramp is built to help wheelchair access. If the ramp forms a triangle with the ground and the height of the ramp is 3 feet while the base is 4 feet, what is the angle at the base if a similar ramp has a height of 6 feet?

• 45 degrees

• 36.87 degrees

• 30 degrees

• 60 degrees

Two buildings are standing next to each other. Building A is 30 meters tall and casts a shadow of 20 meters. Building B is 45 meters tall. If the shadow of Building B is 30 meters, are the triangles formed by the buildings and their shadows similar?

• Yes, the triangles are similar.

• Yes, the triangles are identical.

• No, the triangles are different shapes.

• No, the triangles are not similar.

In triangle MNO, angle M is 70 degrees and angle N is 40 degrees. If triangle PQR is similar to triangle MNO and angle P is 70 degrees, what is angle Q?

• 50 degrees

• 30 degrees

• 60 degrees

• 40 degrees

A kite is flying at a height of 10 meters and casts a shadow of 5 meters. A flagpole casts a shadow of 15 meters. If the height of the flagpole is unknown, can you find it using triangle similarity?

• 20 meters

• 15 meters

• 5 meters

• 30 meters

In triangle STU, angle S is 45 degrees and angle T is 55 degrees. If triangle VWX is similar to triangle STU and angle V is 45 degrees, what is angle W?

• 60 degrees

• 70 degrees

• 90 degrees

• 55 degrees

A ladder leans against a wall, forming a triangle with the ground. If the ladder is 10 feet long and the distance from the wall to the base of the ladder is 6 feet, what is the angle at the wall?

• 90 degrees

• 75 degrees

• 53.13 degrees

• 30 degrees

In triangle ABC, angle A is 30 degrees and angle B is 60 degrees. If triangle DEF is similar to triangle ABC and angle D is 30 degrees, what is angle E?

• 45 degrees

• 90 degrees

• 60 degrees

• 120 degrees