Triangles quiz

All circles are:

In triangle ABC, DE is parallel to BC. If AD/DB = 3/5 and AE = 4.5 cm, then EC is:

If triangle ABC is similar to triangle PQR, then AB/PQ is equal to:

Two triangles are similar if their corresponding angles are equal. This criterion is called:

The sides of two similar triangles are in the ratio 2 : 3. The ratio of their perimeters is:

A 6 m pole casts a 4 m shadow. At the same time, a building casts a 20 m shadow. The height of the building is:

Which pair of triangles with the given sides is similar?

In triangle PQR, angle P = 50 degrees and angle Q = 70 degrees. In triangle XYZ, angle X = 50 degrees and angle Z = 60 degrees. Then:

Two polygons are similar if their corresponding angles are equal and their corresponding sides are:

In triangle ABC, D and E are midpoints of AB and AC. If BC = 10 cm, then DE is:

Give two examples of similar figures and two examples of figures that are not similar. (2 marks)

State whether a square and a rhombus are always similar. Give a reason. (2 marks)

In triangle ABC, DE is parallel to BC with AD = 2 cm, AB = 6 cm and AC = 9 cm. Find AE. (2 marks)

If a line intersects sides AB and AC of a triangle ABC at D and E and is parallel to BC, prove that AD/AB = AE/AC. (2 marks)

In triangle ABC, D lies on AB, E lies on BC and F lies on BE. If DE is parallel to AC and DF is parallel to AE, prove that BF/FE = BE/EC. (2 marks)

ABCD is a trapezium with AB parallel to DC. A line EF parallel to AB meets AD at E and BC at F. Show that AE/ED = BF/FC. (2 marks)

Explain why two equilateral triangles are always similar. (2 marks)

The diagonals of a quadrilateral ABCD intersect at O such that AO/BO = CO/DO. Show that ABCD is a trapezium. (2 marks)

Triangle ABC has sides 6 cm, 8 cm and 10 cm. A similar triangle has its shortest side 9 cm. Find its other sides. (2 marks)

In triangles ABC and DEF, angle A = angle D and AB/DE = AC/DF. Which criterion proves them similar? Draw a rough figure. (2 marks)

In triangle ABC, DE is parallel to BC. If AD = 2.4 cm, AE = 3.2 cm, DE = 2 cm and BC = 5 cm, find BD and CE. (3 marks)

A tree casts a shadow of 15 m when a 1.5 m tall boy standing nearby casts a shadow of 2.5 m. Find the height of the tree. (3 marks)

Triangle ABC is similar to triangle PQR. The perimeter of triangle ABC is 36 cm and that of triangle PQR is 24 cm. If PQ = 10 cm, find AB. (3 marks)

In triangle ABC, D and E are points on AB and AC such that AD = 6 cm, DB = 9 cm, AE = 8 cm and EC = 12 cm. Show that DE is parallel to BC and find BC if DE = 4 cm. (3 marks)

CD and GH are respectively the bisectors of angle ACB and angle EGF such that D and H lie on sides AB and FE of triangles ABC and EFG. If triangle ABC is similar to triangle FEG, and AC = 12 cm, FG = 8 cm and CD = 6 cm, find GH. (3 marks)

Read the passage and answer the questions. Students of a school want to find the height of a tall tree without climbing it. At 10 a.m., they measure the shadow of the tree as 24 m. At the same time, a 1.5 m tall stick held vertically casts a shadow of 2 m. (i) Why are the two triangles formed by the objects and their shadows similar? Name the criterion. (ii) Find the height of the tree. (iii) At noon, the shadow of the stick is 1 m. What will be the length of the tree's shadow then? (5 marks)

Read the passage and answer the questions. An architect makes a scale model of a triangular garden. In the model, the sides of the triangle are 6 cm, 8 cm and 10 cm. The longest side of the actual garden is 50 m. (i) What is the scale factor between the model and the actual garden? (ii) Find the other two sides of the actual garden. (iii) Find the perimeter of the actual garden. (5 marks)

Read the passage and answer the questions. A ladder rests against a wall, and a rod is fixed horizontally between the ladder and the wall, parallel to the ground. The ladder makes triangle ABC with the ground BC and the wall AC, and the rod DE has D on AB and E on AC. AD = 2 m, DB = 3 m and AE = 1.6 m. (i) Which theorem relates the parts of AB and AC here? (ii) Find EC. (iii) Find AC, the height up the wall reached by the ladder. (5 marks)

Read the passage and answer the questions. A photographer enlarges a triangular logo. The original has angles 40, 60 and 80 degrees, and the side opposite 60 degrees is 3 cm. In the enlargement, the side opposite 60 degrees is 7.5 cm. (i) What are the angles of the enlarged logo, and why? (ii) Find the scale factor. (iii) If the side opposite 80 degrees is 3.4 cm in the original, find it in the enlargement. (5 marks)

Read the passage and answer the questions. A street lamp is fixed at a height of 4.5 m. A boy 1.5 m tall stands 6 m from the foot of the lamp post. (i) Draw a rough figure and identify the similar triangles. (ii) Find the length of the boy's shadow. (iii) How far from the foot of the lamp post must he stand so that his shadow is 4 m long, and how much further must he walk? (5 marks)

State and prove the Basic Proportionality Theorem. Draw a neat labelled figure, showing clearly the construction of perpendiculars and the triangles whose areas are compared. (6 marks)

State the converse of the Basic Proportionality Theorem. In triangle ABC, D and E are points on AB and AC such that AD/DB = AE/EC. Draw the figure and explain how the converse helps to prove DE is parallel to BC. Use it to check whether DE is parallel to BC when AD = 1.4 cm, AB = 5.6 cm, AE = 1.8 cm and AC = 7.2 cm. (6 marks)

Explain the AAA, SSS and SAS criteria for similarity of triangles, with one labelled figure for each. Using the AA criterion, prove that if two chords AB and CD of a circle intersect at P inside the circle, then triangle PAC is similar to triangle PDB. (6 marks)

In triangle ABC, AD is the bisector of angle A meeting BC at D. Through C, a line is drawn parallel to DA meeting BA produced at E. Draw the figure and prove that BD/DC = AB/AC (the angle bisector theorem), using the Basic Proportionality Theorem. (6 marks)

Draw a figure of a triangle ABC with DE parallel to BC and D, E on AB, AC. Prove that triangle ADE is similar to triangle ABC. Hence, if AD = 3 cm, DB = 2 cm and BC = 7.5 cm, find DE. Also show that the ratio of the perimeters of the two triangles equals AD/AB. (6 marks)