Moderate Level Worksheet
Very Short Answer Questions (1 Mark Each)
(1) State the SAS criterion for congruence of triangles. If two
Perfect! SAS stands for Side-Angle-Side with the angle between the two sides.
(2) In △PQR, if PQ = PR and ∠Q = 50°, find ∠R. ∠R =
Excellent! In isosceles triangles, base angles are always equal.
(3) Write the symbol used to denote "is similar to."
Correct! The symbol ~ represents similarity between geometric figures.
(4) In △ABC, if ∠A = 90°, AB = AC, name the type of triangle.
Great! It's both right-angled (90°) and isosceles (two equal sides).
(5) Write the ratio of the corresponding sides of two similar triangles if their areas are in the ratio 9 : 16. Side ratio =
Perfect! Side ratio is the square root of the area ratio.
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 △ABC and △PQR, AB = PQ, BC = QR, and CA = RP. Write the criterion for congruence of these triangles. △ABC ≅ △PQR by
Excellent! When all three sides are equal, we use SSS congruence.
(2) Two triangles are similar and the ratio of their corresponding sides is 3 : 4. Find the ratio of their areas. Area ratio =
Perfect! Area ratio is always the square of the side ratio for similar figures.
(3) In △XYZ, ∠X = ∠Y. Write two properties of this triangle.
Property 1: Triangle is
Property 2: Sides
Great! Equal angles make a triangle isosceles with corresponding equal sides.
(4) If △ABC ∼ △DEF and AB = 6 cm, DE = 9 cm, find the ratio of their perimeters. Perimeter ratio =
Excellent! Perimeter ratio equals side ratio for similar triangles.
(5) In △PQR, PQ = PR and S is a point on QR such that PS is perpendicular to QR. Prove that QS = SR.
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) In △ABC, AB = AC and AD is the median. Show that BD = DC.
(2) In △XYZ, XY = XZ and XM is perpendicular to YZ. Show that △XMY ≅ △XMZ.
(3) In △PQR, PS is the bisector of ∠QPR meeting QR at S. Show that
(4) The diagonals of a rhombus bisect each other at right angles. Prove that all four triangles formed are congruent.
(5) In △ABC, AD is the median. Show that
Part B: Objective Questions (1 Mark Each)
Choose the correct answer and write the option (a/b/c/d)
(1) If two triangles have equal corresponding angles, then they are:
(a) Congruent (b) Similar (c) Equal in area (d) None
Correct! Equal corresponding angles make triangles similar (AAA criterion).
(2) Which congruence criterion uses "hypotenuse and one side"?
(a) SSS (b) ASA (c) SAS (d) RHS
Correct! RHS (Right angle-Hypotenuse-Side) uses hypotenuse and one side.
(3) In △DEF, ∠D = 60°, ∠E = 60°, then the triangle is:
(a) Scalene (b) Isosceles (c) Equilateral (d) Right-angled
Correct! If two angles are 60°, the third is also 60°, making it equilateral.
(4) If △ABC ∼ △PQR and
(a) 1 : 2 (b) 2 : 1 (c) 1 : 4 (d) 4 : 1
Correct! Area ratio =
(5) Which of the following is not a similarity criterion for triangles?
(a) AAA (b) SAS (c) SSS (d) ASA
Correct! ASA is for congruence, not similarity. Similarity criteria are AA, SSS, SAS.
(6) If AB = AC in △ABC, then △ABC is:
(a) Scalene (b) Isosceles (c) Equilateral (d) Right-angled
Correct! Two equal sides make a triangle isosceles.
(7) Which criterion proves two triangles similar when two sides are in proportion and the included angle is equal?
(a) SAS similarity (b) AAA similarity (c) SSS similarity (d) RHS similarity
Correct! SAS similarity uses two proportional sides and included angle.
(8) If △LMN ∼ △XYZ and LM = 5 cm, XY = 8 cm, then the ratio
(a) 5 : 8 (b) 8 : 5 (c) 3 : 5 (d) 5 : 3
Correct! All corresponding sides of similar triangles are in the same ratio.
(9) The property "corresponding sides of similar triangles are in proportion" is used in:
(a) Congruence (b) Similarity (c) Both (d) None
Correct! Proportional sides is specifically a property of similarity.
(10) In a right triangle, if altitude is drawn to the hypotenuse, then the two triangles formed are:
(a) Congruent only (b) Similar only (c) Congruent and similar (d) Neither
Correct! The triangles formed are similar to each other and to the original triangle.
Let's distinguish between similarity and congruence criteria!!!
Excellent! You understand the distinction between congruence and similarity criteria.
True or False: Triangle Theorems
Determine whether these advanced triangle statements are True or False: