Triangles

In the figure above, triangle ABC is similar to triangle XYZ. If side XZ measures 10, what is the area of triangle XYZ?

1. 10
2. 22
3. 24
4. 48

Answer: (c) 24

If DE || BC, AD = x, DB = x - 2, AE = x + 2 and EC = x - 1, find the value of x.

1. 4
2. 8
3. 12
4. 5

Answer: (a) 4

Two poles are leaned against a wall such that they make the same angle with the ground. The 18' pole reaches 12 up the wall. How much further up the wall does the 22 pole reach, to the nearest tenth of a foot?

1. 2.7 ft
2. 4.3 ft
3. 6.3 ft
4. 14.7 ft

Answer: (a) 2.7 ft

A tree is reflected in a nearby pond. A person measures the reflection to be 15 feet long when standing 5 feet away from the edge of the pond. The person knows the tree is 25 feet from the edge of the pond. How tall is the tree?

1. 30 ft
2. 35 ft
3. 75 ft
4. 40 ft

Answer: (c) 75 ft

In triangle PQR, a line joining point X on side PQ and point Y on side PR is parallel to side QR. If the ratio PY : YR is 3 : 5 and length PX = 7 cm, then what is the length of side PQ?

1. 10.5 cm
2. 12 cm
3. 14 cm
4. 18.66 cm

Answer: (d) 18.66 cm

In the figure below, lines DG, CF, and BE are parallel. If line segment AB = 6, line segment AE = 9, line segment EF = 10, and line segment FG = 11, what is the length of line AD?

1. 12
2. 20
3. 40
4. 15

Answer: (b) 20

Mia wants to measure the height of a building but she does not have the tools to do so. She noticed that there was a tree located in front of the building so she decided to use her smartness and geometry knowledge. She measured the distance between the tree and the building and found that it was 30 m. She stood in front of the tree and started backing until she could see the top edge of the building from above the tree top. She marked her place and measured it from the tree. It was 5 m. Knowing that the tree's height is 2.8 m and Trisha’s eyes height is 1.6 m. Calculate the building height.

1. 10 m
2. 20 m
3. 15 m
4. 25 m

Answer: (a) 10 m

Triangles ABC and PQR are respectively congruent. If AB = 8 = PQ, BC = 10 = QR and angle B = 35o, then what is the value of ∠P + ∠C?

1. 102o
2. 145o
3. 112o
4. 158o

Answer: (b) 145o

Read the passage and answer the following question: A factory is using an inclined conveyor belt to transport its products from Level 1 to Level 2 which is 3 m above Level 1 as shown by the figure below. The inclined conveyor is supported from one end to Level 1 and from the other end to a post located 8 m away from Level 1 support point. The factory wants to extend its conveyor to reach a new Level 2 which is 9 m above Level 1 while maintaining the inclination angle of the conveyor. Which of the following statements is true regarding triangles △ADE and △ABC?

1. The two triangles are congruent by SSS criterion.
2. The two triangles are congruent by SAS criterion.
3. The two triangles are similar but not congruent.
4. The two triangles are neither similar nor congruent.

Answer: (c) The two triangles are similar but not congruent.

In the trapezium ABCD, AB||CD and AB = 2 CD. Its diagonals intersect at O. If the area of triangle AOB = 84 cm2, find the area of triangle COD.

1. 18 cm2
2. 15 cm2
3. 10 cm2
4. 21 cm2

Answer: (d) 21 cm2