Easy Level Worksheet
Very Short Answer Questions (1 Mark Each)
(1) Define a triangle. A
Perfect! A triangle is the simplest polygon with three sides and three vertices.
(2) Write the sum of all interior angles of a triangle.
Excellent! This is the fundamental angle sum property of triangles.
(3) State the SSS criterion for congruence of triangles. If
Correct! SSS stands for Side-Side-Side congruence criterion.
(4) Write the full form of RHS criterion.
Great! RHS is specifically for right-angled triangles.
(5) What type of triangle has all three sides equal?
Perfect! An equilateral triangle has all sides equal and all angles equal to 60°.
Short Answer Questions (2 Marks Each)
Note: Answer each question with complete proof and clear diagrams. Write down the answers on sheet and submit to the school subject teacher.
(1) Name all the similarity criteria of triangles.
AA criterion:
SSS criterion:
SAS criterion:
Excellent! These are the three main similarity criteria.
(2) In △ABC, if AB = AC, name the type of triangle and write one property.
Type:
Property:
Perfect! In isosceles triangles, angles opposite to equal sides are equal.
(3) State the AAA criterion for similarity of triangles.
If three
Great! AAA criterion is sufficient for similarity but not for congruence.
(4) Draw a rough figure to show △PQR ≅ △XYZ by SSS criterion.
(5) Write the relation between the areas of two similar triangles if ratio of corresponding sides = k. Ratio of areas =
Excellent! Area ratio equals the square of the side ratio.
Long Answer Questions (4 Marks Each)
Note: Answer each question with complete proof and clear diagrams. Write down the answers on sheet and submit to the school subject teacher.
(1) In △PQR, PQ = PR and PS is the bisector of ∠QPR. Prove that QS = SR.
(2) Draw two similar triangles and verify the property of corresponding sides being in proportion.
(3) In △ABC, AD is the median. Show that the median divides the triangle into two smaller triangles of equal area.
(4) Using RHS criterion, prove that two right-angled triangles are congruent if hypotenuse and one side are equal.
(5) Prove that the ratio of areas of two similar triangles is equal to the square of the ratio of their corresponding sides.
Part B: Objective Questions (1 Mark Each)
Choose the correct answer and write the option (a/b/c/d)
(1) The sum of all interior angles of a triangle is:
(a) 90° (b) 180° (c) 270° (d) 360°
Correct! This is the fundamental angle sum property of triangles.
(2) Which criterion is used when three sides of one triangle are equal to three sides of another triangle?
(a) SSS (b) SAS (c) ASA (d) RHS
Correct! SSS (Side-Side-Side) criterion uses three equal sides.
(3) If in two triangles, two angles are equal, then the triangles are:
(a) Congruent (b) Similar (c) Equal in area (d) None
Correct! Two equal angles make triangles similar (third angle automatically equal).
(4) Which of the following is true for similar triangles?
(a) Corresponding sides are equal (b) Corresponding angles are equal (c) Areas are always equal (d) None
Correct! Similar triangles have equal corresponding angles (sides are proportional).
(5) The hypotenuse of a right triangle is equal to the hypotenuse of another right triangle and one side is also equal. The triangles are congruent by:
(a) SSS (b) SAS (c) ASA (d) RHS
Correct! RHS (Right angle-Hypotenuse-Side) is for right triangles.
(6) If two sides and the included angle of one triangle are equal to the corresponding parts of another triangle, the triangles are congruent by:
(a) ASA (b) SAS (c) SSS (d) RHS
Correct! SAS (Side-Angle-Side) uses two sides and included angle.
(7) Which of the following is not a criterion for congruence of triangles?
(a) AAA (b) SSS (c) SAS (d) ASA
Correct! AAA gives similarity, not congruence (triangles can be different sizes).
(8) In an equilateral triangle, each angle is:
(a) 30° (b) 45° (c) 60° (d) 90°
Correct! In equilateral triangles, all angles are equal: 180° ÷ 3 = 60°.
(9) If two triangles are similar, the ratio of their areas is equal to:
(a) Ratio of corresponding sides (b) Square of the ratio of corresponding sides (c) Double the ratio of corresponding sides (d) None
Correct! Area ratio =
(10) In △ABC, if AB = AC, then ∠B is equal to:
(a) ∠A (b) ∠C (c) ∠B (d) None
Correct! In isosceles triangles, base angles are equal (∠B = ∠C).
Let's classify triangles by their properties!!!
Excellent! You understand the classification of triangles.
True or False: Congruence Statements
Determine whether these congruence statements are True or False: