Easy Level Worksheet
Very Short Answer Questions (1 Mark Each)
(1) Define similar triangles. Triangles with
(2) State the basic proportionality theorem (Thales' theorem). If a
Correct! Thales' theorem is fundamental to understanding similarity in triangles.
(3) If two triangles are similar, what can you say about their corresponding angles? They are
Perfect! Corresponding angles of similar triangles are always equal.
(4) What is the ratio of the areas of two similar triangles if their corresponding sides are in the ratio 2:3?
Excellent! The ratio of areas equals the square of the ratio of corresponding sides:
Short Answer Questions (2 Marks Each)
Note: Answer each question with steps and explanation, in 2-3 sentences. Write down the answers on sheet and submit to the school subject teacher.
(1) In triangle ABC, DE ∥ BC, AD = 3 cm, DB = 6 cm, find the ratio
Perfect! By basic proportionality theorem,
(2) In the given figure, △PQR ∼ △XYZ. If PQ = 4 cm, QR = 6 cm, PR = 8 cm, and XY = 6 cm, find YZ. YZ =
Excellent! Since triangles are similar,
(3) Two similar triangles have areas 49
Perfect! If areas are in ratio 49:64, then sides are in ratio
Long Answer Questions (4 Marks Each)
Note: Answer each question with steps and explanation. Write down the answers on sheet and submit to the school subject teacher.
(1) Prove that if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.
(2) In triangle ABC, D and E are points on AB and AC respectively such that DE ∥ BC. Prove that
Part B: Objective Questions (1 Mark Each)
Choose the correct answer and write the option (a/b/c/d)
(1) Two triangles are similar if:
(a) Their areas are equal (b) Their corresponding angles are equal (c) Their corresponding medians are equal (d) Their sides are equal
Correct! Similar triangles have equal corresponding angles and proportional sides.
(2) In similar triangles, the ratio of the corresponding altitudes is equal to:
(a) 1 (b) The square of the sides (c) The ratio of the areas (d) The ratio of the sides
Correct! All corresponding linear measurements are in the same ratio as the sides.
(3) If △ABC ∼ △DEF and AB = 6 cm, DE = 9 cm, then the ratio
(a)
Correct!
(4) The basic proportionality theorem is also known as:
(a) Pythagoras Theorem (b) Converse of Thales' Theorem (c) Thales' Theorem (d) Euclid's Theorem
Correct! Basic proportionality theorem is also called Thales' Theorem.
(5) If the sides of two similar triangles are in the ratio 5:3, then the ratio of their areas is:
(a) 25:9 (b) 5:3 (c) 3:5 (d) 9:25
Correct! The ratio of areas equals the square of the ratio of sides:
(6) In triangle ABC, DE || BC and intersects AB and AC at D and E respectively. Then
(a) Converse of BPT (b) Thales' Theorem (c) Similarity Criterion (d) None of these
Correct! This is the direct statement of Thales' Theorem (Basic Proportionality Theorem).
(7) Which of the following is not a similarity criterion?
(a) SSS (b) SAS (c) SSA (d) AA
Correct! SSA is not a valid similarity criterion. The valid criteria are AAA, SSS, and SAS.
(8) The areas of two similar triangles are 36
(a) 6:8 (b) 3:4 (c) 9:16 (d) 4:3
Correct! If areas are 36:64, then sides are
(9) If two triangles are similar, then the ratio of any two corresponding medians is equal to:
(a) Ratio of the areas (b) Ratio of their sides (c) Ratio of their perimeters (d) 1
Correct! All corresponding linear measurements (sides, medians, altitudes, perimeters) have the same ratio.
(10) If in triangle ABC, a line DE is drawn parallel to BC intersecting AB and AC in D and E respectively, and AD = 3 cm, DB = 2 cm, AE = 4.5 cm, then EC =
(a) 1.5 cm (b) 3 cm (c) 2.5 cm (d) 4 cm
Correct! By BPT:
Similar Triangles Challenge
Determine whether these statements about similar triangles are True or False: