Triangles — Practice Quiz
Karnataka Board · Class 10 · Mathematics
Try a 4-question quiz on Triangles for Karnataka Board Class 10 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, if DE is parallel to BC where D and E are points on AB and AC respectively, and AD = 4 cm, DB = 6 cm, AE = 3 cm, then find EC.
Two triangles ABC and PQR are similar. If AB = 6 cm, BC = 8 cm, AC = 10 cm and PQ = 9 cm, then find QR.
In triangle PQR, if angle P = 60°, angle Q = 80°, and in triangle XYZ, angle X = 60°, angle Y = 80°, then which similarity criterion proves that triangle PQR ~ triangle XYZ?
If triangle ABC ~ triangle DEF with ratio of similarity 2:3, and area of triangle ABC is 16 cm², then find the area of triangle DEF.
Sample Questions
In triangle ABC, D and E are points on sides AB and AC such that DE || BC. If AD = 5 cm, AB = 15 cm, and AC = 18 cm, then find AE.
Show answer
6 cm
Step 1: Given DE || BC, AD = 5 cm, AB = 15 cm, AC = 18 cm. We need to find AE. Step 2: By Basic Proportionality Theorem, DE || BC implies AD/AB = AE/AC. Step 3: Substituting known values: 5/15 = AE/18. Step 4: Simplify the left side: 1/3 = AE/18. Step 5: Cross multiply: AE = 18 × 1/3 = 6 cm.
Two poles of heights 6 m and 11 m stand vertically on a plane ground. If the distance between their feet is 12 m, find the distance between their tops.
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13 m
Step 1: Draw perpendiculars from the top of shorter pole to both the ground and the taller pole. Step 2: This forms a right triangle with horizontal distance 12 m and vertical distance (11-6) = 5 m. Step 3: The distance between tops is the hypotenuse of this right triangle. Step 4: Using Pythagoras theorem: distance² = 12² + 5² = 144 + 25 = 169. Step 5: Therefore, distance = √169 = 13 m.
In triangle PQR, if PQ = 12 cm, QR = 16 cm, and PR = 20 cm, then find the ratio in which the angle bisector from Q divides side PR.
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3:4
Step 1: Given PQ = 12 cm, QR = 16 cm, PR = 20 cm. The angle bisector from Q meets PR at point S. Step 2: By Angle Bisector Theorem, the angle bisector divides the opposite side in the ratio of the other two sides. Step 3: PS/SR = PQ/QR (sides adjacent to the bisected angle). Step 4: Substituting: PS/SR = 12/16 = 3/4. Step 5: Therefore, the angle bisector divides PR in the ratio 3:4.
If triangles ABC and PQR are similar with AB/PQ = 4/9, then what is the ratio of their perimeters?
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4:9
Step 1: Given triangles ABC ~ PQR with AB/PQ = 4/9. Step 2: In similar triangles, all corresponding sides are in the same ratio. Step 3: Therefore, AB/PQ = BC/QR = CA/RP = 4/9. Step 4: Perimeter of ABC/Perimeter of PQR = (AB + BC + CA)/(PQ + QR + RP). Step 5: This equals (AB + BC + CA)/(PQ + QR + RP) = 4/9, since each corresponding side has the same ratio.
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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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