Triangles
ICSE · Class 9 · Mathematics
Flashcards for Triangles — ICSE Class 9 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.
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Get startedProblem: In triangle ABC, side AC is greater than side AB. Which angle is greater: angle B or angle C?
Answer
Step 1: The greater side has the greater angle opposite to it. Step 2: Side AC is opposite angle B. Step 3: Side AB is opposite angle C. Answer: angle B is greater than angle C.
Problem: In triangle ABC, angle C is greater than angle A. Which side is longer: AB or BC?
Answer
Step 1: The greater angle has the greater side opposite to it. Step 2: Angle C is opposite side AB. Step 3: Angle A is opposite side BC. Answer: AB is longer than BC.
Problem: In triangle ABC, AB = AC. What can be said about angle B and angle C?
Answer
Step 1: If any two sides of a triangle are equal, the angles opposite them are equal. Step 2: AB = AC. Step 3: Angle C is opposite AB and angle B is opposite AC. Answer: angle B = angle C.
Problem: In triangle ABC, angle B = angle C. What can be said about AB and AC?
Answer
Step 1: If any two angles of a triangle are equal, the sides opposite them are equal. Step 2: Angle B = angle C. Step 3: Side AC is opposite angle B and side AB is opposite angle C. Answer: AB = AC.
Problem: Find the third angle of a triangle if angle A = 50° and angle B = 60°.
Answer
Step 1: Use the angle sum property. Step 2: angle A + angle B + angle C = 180°. Step 3: 50° + 60° + angle C = 180°. Step 4: angle C = 180° - 110° = 70°. Answer: 70°.
Formula: What is the angle sum property of a triangle?
Answer
Formula: angle A + angle B + angle C = 180°. Meaning: The three interior angles of a triangle always add up to 180°. Quick example: If two angles are 40° and 65°, the third angle is 75° because 180° -…
Problem: One angle of a triangle is 90° and another is 35°. Find the third angle.
Answer
Step 1: The sum of angles in a triangle is 180°. Step 2: 90° + 35° + angle C = 180°. Step 3: angle C = 180° - 125° = 55°. Answer: 55°. Check: 90° + 35° + 55° = 180°.
Problem: If one angle of a triangle is 100°, can the triangle have another obtuse angle?
Answer
Step 1: A triangle cannot have more than one obtuse angle. Step 2: The angles of a triangle add up to 180°. Step 3: After one angle is 100°, only 80° is left for the other two angles. Step 4: Two obtu…
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