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Mathematics · Self Assessment

Practice Test: Congruence, Similarity, Constructions & Loci

A 100-mark paper covering "Congruence & Similarity" and "Constructions & Loci" — multiple choice, true/false, fill-in-the-blank, column matching, and short answer, all auto-graded instantly.

EDUSAMBAM Editorial Team · 45 questions · 100 marks · Instant self-assessment

Questions

100

Marks

Sections

100%

Auto-Graded

Section	Questions	Marks Each	Total
A — Multiple Choice	15	2	30
B — True / False	10	2	20
C — Fill in the Blank	10	2	20
D — Column Matching	5 pairs	2	10
E — Short Answer	5	4	20
Total	45	—	100

Fill-in-the-blank and short-answer questions are checked automatically against accepted answers — exact wording doesn't need to match, but the key term should be present.

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Section A — Multiple Choice

30 marks

15 questions · 2 marks each.

1.Two shapes that are exactly the same shape AND the same size are called:Basic2 pts

A. Similar

B. Symmetrical

C. Regular

D. Congruent

2.Which congruence test requires all three sides to be equal?Basic2 pts

A. SAS

B. SSS

C. ASA

D. RHS

3.For the SAS congruence test, the given angle must be:Intermediate2 pts

A. Included between the two known sides

B. Any angle in the triangle

C. A right angle

D. The largest angle

4.The RHS congruence test can only be used for:Intermediate2 pts

A. Isosceles triangles

B. Equilateral triangles

C. Right-angled triangles

D. Any quadrilateral

5.Two similar triangles have a linear scale factor of 3. Their area ratio is:Advanced2 pts

A. 9

B. 3

C. 6

D. 27

6.Two similar solids have a linear scale factor of 2. Their volume ratio is:Advanced2 pts

A. 2

B. 4

C. 8

D. 6

7.Congruent shapes are a special case of similar shapes where the scale factor is:Intermediate2 pts

A. 0

B. 1

C. 2

D. Undefined

8.A formal geometric construction may only use:Basic2 pts

A. A protractor and ruler

B. A protractor only

C. A calculator

D. A ruler and a pair of compasses

9.To construct a perpendicular bisector, the compass radius must be:Intermediate2 pts

A. Exactly the length of the segment

B. Less than a quarter of the segment

C. More than half the length of the segment

D. It does not matter

10.The locus of points a fixed distance from a single point is a:Basic2 pts

A. Circle

B. Straight line

C. Triangle

D. Square

11.The locus of points equidistant from two fixed points A and B is:Intermediate2 pts

A. A circle around A

B. The line segment AB itself

C. An angle bisector

D. The perpendicular bisector of AB

12.The locus of points equidistant from two straight lines meeting at a vertex is:Intermediate2 pts

A. The perpendicular bisector of one line

B. The angle bisector between them

C. A line parallel to both

D. A circle

13.The locus of points a fixed distance from a straight line segment (including its ends) is:Advanced2 pts

A. A single circle

B. Two parallel lines with semicircular ends (a "stadium" shape)

C. A single straight line

D. A square

14.Construction arcs on a finished diagram should be:Basic2 pts

A. Erased before submitting

B. Measured with a protractor

C. Drawn in pen only

D. Left visible, as evidence of an accurate method

15.Bisecting a constructed 90° angle gives an angle of:Intermediate2 pts

A. 90°

B. 30°

C. 45°

D. 60°

Section B — True / False

20 marks

10 questions · 2 marks each.

16."SSA" (two sides and a non-included angle) is a valid congruence test on its own.Advanced2 pts

True

False

17.Similarity requires all corresponding sides to be in the same ratio, not just one pair.Intermediate2 pts

True

False

18.A linear scale factor of 3 gives an area ratio of 3 (not squared).Advanced2 pts

True

False

19.Two triangles with two pairs of equal angles (AA) are similar.Intermediate2 pts

True

False

20.Congruent triangles always have the same area.Basic2 pts

True

False

21.A protractor is required in a formal ruler-and-compass construction.Basic2 pts

True

False

22.The angle bisector of an angle divides it exactly in half.Basic2 pts

True

False

23.The plural of "locus" is "loci".Basic2 pts

True

False

24.The locus of points equidistant from two points is a circle.Intermediate2 pts

True

False

25.Erasing construction arcs before submitting a diagram is good practice.Intermediate2 pts

True

False

Section C — Fill in the Blank

20 marks

10 questions · 2 marks each. Type the missing word or term.

26.Two shapes with the same shape but a different size are called ______.Basic2 pts

27.The congruence test using two sides and the included angle is called ______.Intermediate2 pts

28.If two similar shapes have a linear scale factor of k, their area ratio is k______.Advanced2 pts

29.If two similar solids have a linear scale factor of k, their volume ratio is k______.Advanced2 pts

30.The similarity test using only two pairs of equal angles is called ______.Intermediate2 pts

31.A geometric construction uses only a ruler and a pair of ______.Basic2 pts

32.The line that crosses a segment at 90° through its exact midpoint is called the ______ bisector.Intermediate2 pts

33.The set of all points satisfying a given rule is called a ______.Basic2 pts

34.The locus of points a fixed distance from a single point is a ______.Basic2 pts

35.Bisecting a constructed 60° angle gives an angle of ______ degrees.Intermediate2 pts

Section D — Column Matching

10 marks

Match each term to its correct definition. Use the ▲▼ buttons to reorder Column B.

36–40.Match each term to its correct definition.Advanced10 pts

Column A

SSS

RHS

Angle bisector

Perpendicular bisector

Locus

Column B

A line crossing a segment at 90° through its exact midpoint

All three sides of two triangles are equal

The complete set of points satisfying a given rule

A right angle, the hypotenuse, and one other side are equal

A line that divides an angle exactly in half

Section E — Short Answer

20 marks

5 questions · 4 marks each. Answer in one or two sentences.

41.Explain why "SSA" is not a reliable test for triangle congruence.Advanced4 pts

42.Describe how the area and volume of two similar shapes relate to their linear scale factor.Advanced4 pts

43.Describe the construction method for a perpendicular bisector of a line segment.Advanced4 pts

44.Explain what is meant by "the locus of points equidistant from two lines".Intermediate4 pts

45.Describe the shape of the locus of points a fixed distance from a straight line segment.Advanced4 pts

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