Triangles — Flashcards
Telangana Board · Class 9 · Mathematics
20 flashcards for Triangles (Telangana Board Class 9 Mathematics) to test yourself on key terms and facts. Sample: "In triangle ABC, AB = 5 cm, BC = 7 cm"
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In triangle ABC, AB = 5 cm, BC = 7 cm, and angle B = 60°. In triangle PQR, PQ = 5 cm, QR = 7 cm, and angle Q = 60°. Are these triangles congruent? Prove it.
Answer
Step 1: Identify given information - AB = PQ = 5 cm, BC = QR = 7 cm, ∠B = ∠Q = 60°. Step 2: Check which congruence rule applies - Two sides and included angle are equal. Step 3: Apply SAS rule - In △A…
Solve: In triangle ABC, AB = AC = 8 cm. If angle A = 40°, find angles B and C.
Answer
Step 1: Identify triangle type - AB = AC, so triangle ABC is isosceles. Step 2: Apply isosceles triangle property - Angles opposite to equal sides are equal, so ∠B = ∠C. Step 3: Use angle sum property…
In right triangle ABC with right angle at C, AC = 3 cm and BC = 4 cm. In right triangle PQR with right angle at R, PR = 3 cm and QR = 4 cm. Prove these triangles are congruent.
Answer
Step 1: Find hypotenuses using Pythagoras - AB = √(3² + 4²) = √25 = 5 cm, PQ = √(3² + 4²) = 5 cm. Step 2: Identify given - ∠C = ∠R = 90°, AC = PR = 3 cm, BC = QR = 4 cm, AB = PQ = 5 cm. Step 3: Apply …
When do you use the SSS congruence rule? Give an example with solution.
Answer
Use SSS rule when all three sides of one triangle are equal to corresponding sides of another triangle. Example: Triangle ABC has sides 6 cm, 8 cm, 10 cm. Triangle DEF has sides 6 cm, 8 cm, 10 cm. Sol…
In triangle PQR, PQ = 7 cm, QR = 5 cm, and PR = 9 cm. Which angle is the largest and why?
Answer
Step 1: Identify the longest side - PR = 9 cm is the longest side. Step 2: Apply theorem - In a triangle, the angle opposite to the longest side is the largest angle. Step 3: Find opposite angle - The…
Check if a triangle can be formed with sides 3 cm, 7 cm, and 12 cm. Justify your answer.
Answer
Step 1: Apply triangle inequality theorem - Sum of any two sides must be greater than the third side. Step 2: Check all combinations - (i) 3 + 7 = 10 < 12 ✗ (ii) 3 + 12 = 15 > 7 ✓ (iii) 7 + 12 = 19 > …
In triangle ABC, angle A = 30°, angle B = 80°, and AB = 6 cm. In triangle PQR, angle P = 30°, angle Q = 80°, and PQ = 6 cm. Are these triangles congruent?
Answer
Step 1: Find third angles - In △ABC: ∠C = 180° - 30° - 80° = 70°. In △PQR: ∠R = 180° - 30° - 80° = 70°. Step 2: Identify given information - ∠A = ∠P = 30°, ∠B = ∠Q = 80°, AB = PQ = 6 cm. Step 3: Check…
Formula for congruent triangles: List all congruence rules with their conditions.
Answer
1. SAS (Side-Angle-Side): Two sides and included angle equal. Example: AB = PQ, ∠B = ∠Q, BC = QR → △ABC ≅ △PQR. 2. ASA (Angle-Side-Angle): Two angles and included side equal. 3. SSS (Side-Side-Side): …
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