Triangles — Practice Quiz
Karnataka Board · Class 9 · Mathematics
Try a 4-question quiz on Triangles for Karnataka Board Class 9 Mathematics: tap an answer to check it and see why. 45 questions in the full chapter test.
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Quick Quiz: Triangles
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In triangle ABC, AB = 5 cm, BC = 7 cm, and AC = 5 cm. What type of triangle is ABC, and what can you conclude about its angles?
Two triangles PQR and XYZ have PQ = 6 cm, QR = 8 cm, angle Q = 45°, XY = 6 cm, YZ = 8 cm, and angle Y = 45°. Are these triangles congruent by SAS rule?
In triangle ABC, AD is the angle bisector of angle A and also perpendicular to BC. If AB = 8 cm, what is the length of AC?
If triangle ABC ≅ triangle PQR under the correspondence A ↔ P, B ↔ Q, C ↔ R, and AB = 7 cm, BC = 9 cm, what is the length of QR?
Sample Questions
In a right triangle ABC with right angle at C, if AB = 10 cm and BC = 6 cm, what is the length of AC using Pythagoras theorem?
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8 cm
Step 1: Given right triangle ABC with right angle at C, AB = 10 cm (hypotenuse), BC = 6 cm. Step 2: Apply Pythagoras theorem: AB² = AC² + BC². Step 3: Substitute values: 10² = AC² + 6², which gives 100 = AC² + 36. Step 4: Solve for AC: AC² = 100 - 36 = 64, so AC = √64 = 8 cm.
Two right triangles have hypotenuse 13 cm and one side 5 cm each. By which congruence rule are these triangles congruent?
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RHS rule
Step 1: Given two right triangles with equal hypotenuse (13 cm each) and one equal side (5 cm each). Step 2: Both triangles have a right angle (90°). Step 3: RHS (Right angle-Hypotenuse-Side) congruence rule states that if hypotenuse and one side of one right triangle equal hypotenuse and one side of another right triangle, they are congruent. Step 4: Since we have equal hypotenuses and one equal side in both right triangles, they are congruent by RHS rule.
In triangle PQR, if PQ = PR and angle Q = 35°, what is the measure of angle R?
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35°
Step 1: Given triangle PQR with PQ = PR (isosceles triangle) and angle Q = 35°. Step 2: In an isosceles triangle, angles opposite to equal sides are equal. Step 3: Since PQ = PR, the angles opposite to these sides are angle R and angle Q respectively. Step 4: Therefore, angle R = angle Q = 35°.
If two triangles ABC and DEF are congruent by ASA rule, and angle A = 60°, AB = 8 cm, angle B = 70°, what is the value of angle E in triangle DEF?
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70°
Step 1: Given triangles ABC and DEF are congruent by ASA rule with angle A = 60°, AB = 8 cm, angle B = 70°. Step 2: For ASA congruence, the correspondence is typically A ↔ D, B ↔ E, C ↔ F when sides AB and DE are equal. Step 3: In congruent triangles, corresponding angles are equal. Step 4: Since angle B corresponds to angle E, angle E = angle B = 70°.
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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
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
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