Triangles — Flashcards
Karnataka Board · Class 9 · Mathematics
20 flashcards for Triangles (Karnataka Board Class 9 Mathematics) to test yourself on key terms and facts. Sample: "In triangle ABC, AB = 5 cm, AC = 5 cm.
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In triangle ABC, AB = 5 cm, AC = 5 cm, and BC = 6 cm. Find the measures of 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: Let ∠B = ∠C = x. Step …
Prove that triangles ABC and DEF are congruent if AB = DE = 4 cm, BC = EF = 3 cm, and ∠B = ∠E = 90°.
Answer
Step 1: Identify given information → AB = DE = 4 cm, BC = EF = 3 cm, ∠B = ∠E = 90°. Step 2: Check congruence rule → We have two sides and included angle. Step 3: Apply SAS rule → In △ABC and △DEF: AB …
In triangle PQR, PQ = 7 cm, QR = 7 cm, and PR = 8 cm. If QS is the altitude to PR, find the length of PS.
Answer
Step 1: Identify triangle type → PQ = QR = 7 cm, so triangle PQR is isosceles. Step 2: Property of isosceles triangle → Altitude from vertex angle bisects the base. Step 3: Since QS is altitude to PR,…
When do you use the ASA congruence rule? Give a worked example.
Answer
Use ASA when: Two angles and included side of one triangle equal two angles and included side of another triangle. Example: In △ABC and △XYZ, if ∠A = ∠X = 60°, ∠B = ∠Y = 50°, and AB = XY = 5 cm. Step …
Solve: In △ABC, AB = AC = 10 cm and BC = 12 cm. Find the area of the triangle.
Answer
Step 1: Identify triangle type → AB = AC, so isosceles triangle. Step 2: Draw altitude AD to BC → D bisects BC, so BD = DC = 6 cm. Step 3: Use Pythagoras in △ABD → AD² + BD² = AB², so AD² + 6² = 10², …
Prove: If two triangles have all three sides equal, they are congruent. State the rule used.
Answer
Step 1: State the rule → SSS (Side-Side-Side) Congruence Rule. Step 2: Given → In △ABC and △DEF: AB = DE, BC = EF, CA = FD. Step 3: Apply SSS rule → Since all three corresponding sides are equal, △ABC…
In right triangle ABC with ∠C = 90°, if AB = 13 cm and BC = 5 cm, find AC and verify using congruence.
Answer
Step 1: Apply Pythagoras theorem → AB² = AC² + BC², so 13² = AC² + 5². Step 2: Calculate AC → 169 = AC² + 25, so AC² = 144, therefore AC = 12 cm. Step 3: Verify dimensions → We have a 5-12-13 right tr…
When do you use RHS congruence rule? Solve: Two right triangles have hypotenuse 10 cm and one side 6 cm. Are they congruent?
Answer
Use RHS when: Two right triangles have equal hypotenuse and one equal side. Solution: Step 1: Given → Both triangles have hypotenuse = 10 cm, one side = 6 cm, and one right angle. Step 2: Find third s…
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Sources & Official References
- Karnataka SSLC — kseeb.kar.nic.in
- Dept of Pre-University Education, Karnataka
- National Education Policy 2020 — education.gov.in
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