Similarity and Congruence: Master Geometry with Interactive Quizzes

Question 1

If two triangles have corresponding angles that are congruent, they are:

Accepted Answer

Similar

Answer

Congruent

Answer

Neither similar nor congruent

Answer

Only similar if their sides are also congruent

Question 2

Two similar triangles have a scale factor of 3. What is the ratio of their areas?

Accepted Answer

9:1

Answer

1:3

Answer

3:1

Answer

1:9

Question 3

In a circle, if two chords are congruent, what are their properties?

Accepted Answer

Both their arcs and central angles are congruent

Answer

Their arcs are congruent

Answer

Their central angles are congruent

Answer

Neither their arcs nor central angles are congruent

Question 4

In a right triangle, the hypotenuse is 10 cm and one leg is 6 cm. What is the length of the other leg?

Accepted Answer

8 cm

Answer

4 cm

Answer

6 cm

Answer

10 cm

Question 5

What is the primary distinction between congruent and similar figures?

Accepted Answer

Similar figures share the same shape but may vary in size, while congruent figures have identical shape and size.

Answer

Similar figures have the same size but may vary in shape, while congruent figures have identical shape and size.

Answer

Similar figures have the same shape and size, while congruent figures have different shapes and sizes.

Answer

Similar figures have different shapes and sizes, while congruent figures have the same size but different shapes.

Question 6

If two figures have the same shape, but different sizes, they are considered:

Accepted Answer

Similar

Answer

Congruent

Answer

Equilateral

Answer

Isosceles

Question 7

The ratio of corresponding side lengths of two similar triangles is called the:

Accepted Answer

Similarity ratio

Answer

Scale factor

Answer

Proportionality constant

Answer

Geometric mean

Question 8

Which theorem states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent?

Accepted Answer

Side-Angle-Side (SAS) Theorem

Answer

Side-Side-Angle (SSA) Theorem

Answer

Angle-Side-Angle (ASA) Theorem

Answer

Angle-Angle-Side (AAS) Theorem

Question 9

A transformation that does not alter the size or shape of a figure is called a:

Accepted Answer

Rigid transformation

Answer

Non-rigid transformation

Answer

Linear transformation

Answer

Affine transformation

Question 10

If the scale factor of two similar polygons is 3, what is the ratio of their areas?

Accepted Answer

9:1

Answer

1:1

Answer

1:3

Answer

3:1

Question 11

In a dilation, the point that remains fixed is known as the:

Accepted Answer

Center of dilation

Answer

Point of rotation

Answer

Point of symmetry

Answer

Point of translation

Question 12

Which of the following transformations will always result in a similar figure?

Accepted Answer

Dilation

Answer

Translation

Answer

Rotation

Answer

Reflection over a line

Question 13

A regular hexagon has a side length of 4 cm. What is the perimeter of the hexagon?

Accepted Answer

24 cm

Answer

16 cm

Answer

20 cm

Answer

28 cm

Question 14

Which transformation always preserves similarity but not necessarily congruence?

Accepted Answer

Dilation

Answer

Rotation

Answer

Reflection

Answer

Translation

Question 15

Which of the following statements about similar triangles is TRUE?

Accepted Answer

Their corresponding heights are proportional to their corresponding bases.

Answer

Their corresponding medians are equal.

Question 16

Which theorem states that if two lines are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel?

Accepted Answer

Alternate Interior Angles Theorem

Question 17

In a 30-60-90 triangle, what is the ratio of the length of the shortest side to the length of the hypotenuse?

Accepted Answer

1:√3

Answer

√3:1

Question 18

Area of Congruent Triangles: If triangle PQR is congruent to triangle TUV, and the area of triangle PQR is 24 square units, what is the area of triangle TUV?

Accepted Answer

24 square units

Answer

12 square units

Answer

48 square units

Answer

96 square units

Question 19

Non-Property of a Rectangle: Which characteristic is not a property of a rectangle?

Accepted Answer

All angles are acute angles.

Answer

Opposite sides are congruent.

Answer

Diagonals are congruent and perpendicular bisectors.

Answer

Opposite angles are supplementary.

Question 20

Which of the following is NOT a defining characteristic of congruent figures?

Accepted Answer

Corresponding sides that are proportional

Answer

Identical size and shape

Answer

Matching angles that are congruent

Answer

Ability to be perfectly overlaid on each other

Question 21

In a scaled drawing, the ratio between the length of a line segment in the drawing and the corresponding length in the actual object is known as:

Accepted Answer

Scale factor

Answer

Similarity ratio

Answer

Reduction ratio

Answer

Congruence factor

Question 22

Given a triangle with sides measuring 3, 4, and 5 units, what is the scale factor if its corresponding image has sides measuring 9, 12, and 15 units?

Accepted Answer

2

Answer

3

Answer

4

Answer

Cannot be determined

Question 23

In a similar rectangle, the ratio of the diagonal's length to the shorter side's length is:

Accepted Answer

√2

Answer

2

Answer

√3

Answer

3

Question 24

Given that the diagonals of a parallelogram bisect each other, which of the following is NOT a valid conclusion?

Accepted Answer

The parallelogram is a square

Answer

The parallelogram is a rectangle

Answer

The parallelogram is a rhombus

Answer

The diagonals are congruent

Question 25

Which theorem can be applied to demonstrate the similarity of two triangles based solely on their side lengths?

Accepted Answer

SSS Similarity Theorem

Answer

SAS Similarity Theorem

Answer

AA Similarity Theorem

Answer

HL Similarity Theorem

Question 26

If two triangles have corresponding side lengths in the ratio 3:2 and their corresponding angles are congruent, what type of similarity do they have?

Accepted Answer

Similar

Answer

Congruent

Answer

Neither similar nor congruent

Answer

Complementary

Question 27

Which transformation preserves both distance and angle measures?

Accepted Answer

Translation

Answer

Rotation

Answer

Reflection

Answer

Dilation

Question 28

Two triangles have side lengths of 6 cm, 8 cm, and 10 cm, and 3 cm, 4 cm, and 5 cm, respectively. Determine if the triangles are similar.

Accepted Answer

Yes

Answer

No

Answer

Cannot be determined from the given information

Question 29

Which of the following best describes the relationship between the diagonal of a rectangle and its sides?

Accepted Answer

The diagonal is a hypotenuse of a right triangle formed by the sides.

Answer

The diagonal is equal to the sum of the lengths of the sides.

Answer

The diagonal is proportional to the length of the sides.

Answer

The diagonal bisects the sides at right angles.

Question 30

Which of the following is NOT a property of similar figures?

Accepted Answer

Corresponding medians are equal.

Answer

Corresponding angles are congruent.

Answer

Corresponding sides are proportional.

Answer

Corresponding perimeters are proportional.

Question 31

Similar figures have the same shape, but different sizes. True or False?

Accepted Answer

True

Answer

False

Question 32

In a scale drawing, the ratio of the length of a line segment on the drawing to the corresponding length of the line segment in the actual object is known as the:

Accepted Answer

Scale factor

Answer

Similarity ratio

Answer

Congruence ratio

Answer

Proportionality constant

Question 33

Area is a property of congruent figures.

Accepted Answer

True

Answer

False

Question 34

If two triangles have corresponding sides that are proportional, they are:

Accepted Answer

Similar

Answer

Congruent

Answer

Isosceles

Answer

Scalene

Question 35

Which of the following quadrilaterals is not necessarily similar to a rectangle?

Accepted Answer

Trapezoid

Answer

Square

Answer

Parallelogram

Answer

Rhombus

Question 36

If two triangles have the same shape but not the same size, they are:

Accepted Answer

Similar

Answer

Congruent

Answer

Isosceles

Answer

Scalene

Question 37

Congruent figures can be superimposed on each other without any gaps or overlaps.

Accepted Answer

True

Answer

False

Question 38

If the ratio of the side lengths of two similar triangles is 2:3, what is the ratio of their areas?

Accepted Answer

9:4

Answer

2:3

Answer

3:2

Answer

4:9

Question 39

Which of the following is NOT a characteristic of congruent figures?

Accepted Answer

Same orientation

Answer

Same angle measures

Answer

Same side lengths

Answer

Same area

Question 40

Which of the following statements is NOT a consequence of the Pythagorean Theorem?

Accepted Answer

The sum of the interior angles of a triangle is 180 degrees.

Answer

The square of the hypotenuse is equal to the sum of the squares of the legs.

Answer

A triangle with three equal sides is equilateral.

Answer

A triangle with a right angle is a right triangle.

Question 41

What is the final step in proving triangles congruent using the Side-Side-Side (SSS) congruence theorem?

Accepted Answer

Show that all three sides are equal

Answer

Show that one side is equal

Answer

Show that two sides are equal

Answer

Show that one angle is equal

Question 42

If two lines intersect at a point and their slopes are equal, what is the relationship between the lines?

Accepted Answer

Parallel

Answer

Perpendicular

Answer

Intersecting

Answer

More information is needed

Question 43

Which formula calculates the area of a parallelogram?

Accepted Answer

Area = (1/2) x base x height

Answer

Area = base x height

Answer

Area = π x radius²

Answer

Area = length x width

Question 44

How can you determine if two triangles are similar but not congruent?

Accepted Answer

Check if the side lengths are proportional

Answer

Check if the corresponding angles are equal

Answer

Check if the areas are equal

Answer

Check if the perimeters are equal

Question 45

If two triangles have congruent corresponding angles but NON-proportional sides, what can you conclude?

Accepted Answer

Neither congruent nor similar triangles.

Answer

Congruent triangles.

Answer

Similar triangles.

Answer

Isosceles triangles.

Question 46

What is the ratio of areas for two congruent squares?

Accepted Answer

1:1

Answer

2:1

Answer

1:2

Answer

Cannot be determined given information.

Question 47

What is the relationship between the perimeters of two similar rectangles?

Accepted Answer

Proportional to their scale factor.

Answer

Equal perimeters.

Answer

Proportional to the square of their scale factor.

Answer

Proportional to their areas.

Question 48

Which statement about similar figures is accurate?

Accepted Answer

Same shape, may not be same size.

Answer

Same size, may not be same shape.

Answer

Both same shape and size.

Answer

Always congruent figures.

Question 49

A scale drawing of a building has a scale of 1:500. If the height of the building on the drawing is 15 cm, what is its actual height?

Accepted Answer

60 m

Answer

6 m

Answer

600 m

Answer

6 km