Congruent Figures Worksheet
A Grade 10 Math worksheet covering congruent figures, including properties, proofs, and transformations.
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Congruent Figures Worksheet
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Read each question carefully and answer to the best of your ability. Show all your work for full credit.
1. Which of the following statements is true about congruent figures?
They have the same shape but different sizes.
They have the same size but different shapes.
They have both the same shape and the same size.
They are always oriented in the same direction.
2. If triangle ABC is congruent to triangle DEF (ΔABC ≅ ΔDEF), which of the following is NOT necessarily true?
AB = DE
∠B = ∠E
Area of ΔABC = Area of ΔDEF
ΔABC is a reflection of ΔDEF
1. All squares are congruent.
True
False
2. If two triangles have the same perimeter, they must be congruent.
True
False
1. Two figures are if they have the same size and shape.
2. The symbol for congruence is .
3. A sequence of rigid motions (translations, rotations, reflections) maps one congruent figure onto another. This is known as the definition of congruence.
1. Consider the two triangles shown below. Are they congruent? Justify your answer using congruence postulates.
2. Describe the sequence of rigid transformations that can map Triangle ABC with vertices A(1,1), B(4,1), C(1,3) to Triangle A'B'C' with vertices A'(-1,-1), B'(-4,-1), C'(-1,-3).
Match each congruence postulate with its description.
1. SSS
a. Two angles and the included side are congruent.
2. SAS
b. All three sides are congruent.
3. ASA
c. Two sides and the included angle are congruent.
4. AAS
d. Two angles and a non-included side are congruent.
Given: AD || BC, AD ≅ BC
Prove: ΔABD ≅ ΔCDB