Congruent Triangles: Side Lengths & Real-World Applications

Two triangles, ABC and DEF, are congruent. If the length of side AB is 8 cm and side DE is 8 cm, what can you conclude about the lengths of sides AC and DF if they are also congruent?

• The lengths of sides AC and DF are also equal.

• The lengths of sides AC and DF are different.

• Side AC is longer than side DF.

• Side DF is shorter than side AC.

A park is designed in the shape of two congruent triangular sections. If one section has a base of 10 meters and a height of 6 meters, what is the area of one section?

• 20 square meters

• 25 square meters

• 15 square meters

• 30 square meters

Triangle GHI is congruent to triangle JKL. If the length of side GH is 5 cm and side JK is 5 cm, and the length of side HI is 12 cm, what is the length of side KL?

• 8 cm

• 15 cm

• 12 cm

• 10 cm

In a triangular garden, two sides are congruent and measure 7 feet each. If the perimeter of the garden is 25 feet, what is the length of the third side?

• 5 feet

• 9 feet

• 13 feet

• 11 feet

A ladder leans against a wall, forming two congruent right triangles with the ground. If the height of the wall is 9 feet and the distance from the wall to the base of the ladder is 12 feet, what is the length of the ladder?

• 10 feet

• 15 feet

• 18 feet

• 12 feet

Two congruent triangles are used to create a roof. If the base of each triangle is 15 feet and the height is 10 feet, what is the total area of the roof?

• 100 square feet

• 150 square feet

• 200 square feet

• 75 square feet

In a construction project, two triangular supports are congruent. If one support has a base of 4 meters and a height of 3 meters, what is the height of the other support if it is also congruent?

• 5 meters

• 2 meters

• 4 meters

• 3 meters

A triangular flag is made of two congruent triangles. If the area of one triangle is 20 square inches, what is the total area of the flag?

• 30 square inches

• 50 square inches

• 10 square inches

• 40 square inches

Triangle MNO is congruent to triangle PQR. If the length of side MN is 6 cm and side PQ is 6 cm, and the length of side NO is 8 cm, what is the length of side QR?

• 6 cm

• 10 cm

• 8 cm

• 4 cm

A triangular piece of land has two sides that are congruent and measure 10 meters each. If the angle between these two sides is 60 degrees, what is the length of the third side using the Law of Cosines?

• 10 meters

• 15 meters

• 12 meters

• 8 meters