alleryTriangle sides 3, 4, 5 and 6, 8, 10 are proportional. Which test confirms similarity?
- RHS
- SAS
- AA
- SSS
Show answer and solution
Correct answer: D. SSS
All three corresponding side ratios equal 1:2, so SSS confirms similarity.
ICSE Class 10 Geometry: Similarity, Circles & Loci — practice questions
Explore 121 free Geometry: Similarity, Circles & Loci questions in ICSE Class 10 Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
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Showing questions 1–30 of 121.
Triangle sides 3, 4, 5 and 6, 8, 10 are proportional. Which test confirms similarity?Read the answer and worked solution →Two triangles have angles 40° and 70° in common. Which condition proves they are similar?Read the answer and worked solution →Two side pairs are in ratio 2:3 and their included angles are equal. Which test applies?Read the answer and worked solution →Similar triangles have corresponding sides in ratio 3:5. What is the ratio of their areas?Read the answer and worked solution →The areas of two similar triangles are 16:49. Find their corresponding side ratio.Read the answer and worked solution →A model uses 4 cm for an actual length of 2 m. What is its scale?Read the answer and worked solution →In triangle ABC, D lies on AB with AD:DB=2:3 and DE is parallel to BC. Find AE:EC.Read the answer and worked solution →A line parallel to one side of a triangle cuts the other two sides in what relationship?Read the answer and worked solution →Two similar triangles have side scale factor 2:5. If the smaller perimeter is 18 cm, find the larger perimeter.Read the answer and worked solution →One triangle has sides 4, 6, 8; another has sides 6, 9, 12. Are they similar?Read the answer and worked solution →Equal angles and proportional sides, but unequal sizes: how are the triangles related?Read the answer and worked solution →A 1.5 m pole casts a 2 m shadow. A tree casts an 8 m shadow at the same time. How tall is it?Read the answer and worked solution →A map scale is 1:25,000. What real distance does 6 cm represent?Read the answer and worked solution →In similar triangles, corresponding angles are 55° and 55°. What can be said about those angles?Read the answer and worked solution →A drone stays 5 km from launch point P. What path bounds its travel?Read the answer and worked solution →At a junction of two straight roads, where are sites equally far from both?Read the answer and worked solution →Inside the acute angle between two lines, where can a point be equally far from both?Read the answer and worked solution →Which line has sites equally far from towns A and B?Read the answer and worked solution →Equal arcs at A, B meet at P, Q. What line is PQ?Read the answer and worked solution →Which construction marks all points 4 cm from a fixed point C?Read the answer and worked solution →3 cm from O and equally far from A, B: which loci?Read the answer and worked solution →Two centres are 5 cm apart; circles have radii 3 cm and 4 cm. How many points do they share?Read the answer and worked solution →A circle of radius 6 cm is centred at the crossing of two lines. How many points also lie on their angle bisectors?Read the answer and worked solution →M is the midpoint of AB. How many points are 5 cm from M and equally distant from A and B?Read the answer and worked solution →What curve contains every point exactly 8 cm from a marked centre C?Read the answer and worked solution →A central angle is 100°. What inscribed angle subtends the same arc?Read the answer and worked solution →An inscribed angle is 84°. Find the central angle on the same arc.Read the answer and worked solution →A triangle is drawn with one side as a circle’s diameter. What is the angle opposite that side?Read the answer and worked solution →Angles at two points on the same segment subtend one chord. One is 38°. Find the other.Read the answer and worked solution →A cyclic quadrilateral has one interior angle of 112°. Find its opposite angle.Read the answer and worked solution →
Worked practice questions
Two triangles have angles 40° and 70° in common. Which condition proves they are similar?
- SSS
- SAS
- RHS
- AA
Show answer and solution
Correct answer: D. AA
Two matching angles suffice for AA similarity.
Two side pairs are in ratio 2:3 and their included angles are equal. Which test applies?
- SSS
- SAS
- AA
- RHS
Show answer and solution
Correct answer: B. SAS
Two proportional sides with equal included angles satisfy SAS.
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