Similar And Congruent Triangles Quiz!

1. Is the following triangle similar?

Yes, they are similar (SSS).

No, they're not similar.

Yes, they're similar (SAS)

Cannot be determined.

The given answer states that the triangles are similar based on the SSS (Side-Side-Side) similarity criterion. This criterion states that if the corresponding sides of two triangles are proportional, then the triangles are similar. Since the answer states that the triangles are similar, it implies that the corresponding sides of the triangles are proportional, satisfying the SSS criterion. Therefore, the answer concludes that the given triangles are similar.

Explanation

The given answer states that the triangles are similar based on the SSS (Side-Side-Side) similarity criterion. This criterion states that if the corresponding sides of two triangles are proportional, then the triangles are similar. Since the answer states that the triangles are similar, it implies that the corresponding sides of the triangles are proportional, satisfying the SSS criterion. Therefore, the answer concludes that the given triangles are similar.

2. When corresponding sides of two polygons are proportional, they are similar.

True

False

When corresponding sides of two polygons are proportional, it means that the ratio of the lengths of the corresponding sides is the same for all pairs of corresponding sides. This is a key property of similar figures. Therefore, if the corresponding sides of two polygons are proportional, it implies that the polygons are similar. Hence, the statement "When corresponding sides of two polygons are proportional, they are similar" is true.

Explanation

When corresponding sides of two polygons are proportional, it means that the ratio of the lengths of the corresponding sides is the same for all pairs of corresponding sides. This is a key property of similar figures. Therefore, if the corresponding sides of two polygons are proportional, it implies that the polygons are similar. Hence, the statement "When corresponding sides of two polygons are proportional, they are similar" is true.

3. Two Line segments are congruent if they have the same length.

True

False

Two line segments are congruent if they have the same length. This means that their measurements are equal, and they can be superimposed on each other without any gaps or overlaps. If two line segments have different lengths, they are not congruent. Therefore, the statement "Two line segments are congruent if they have the same length" is true.

Explanation

Two line segments are congruent if they have the same length. This means that their measurements are equal, and they can be superimposed on each other without any gaps or overlaps. If two line segments have different lengths, they are not congruent. Therefore, the statement "Two line segments are congruent if they have the same length" is true.

4. Complete each proportion. AB / BM = ? / CD

MD

BM

AB

AC

The answer AC is correct because in a proportion, the product of the means (AB and CD) is equal to the product of the extremes (AC and BM).

Explanation

The answer AC is correct because in a proportion, the product of the means (AB and CD) is equal to the product of the extremes (AC and BM).

5. The figure below shows the length of side DC equal to 120 units and the length of side DB equal to 160 units. What is the length of segment AC?

140 units.

180 units.

160 units.

Cannot be determined.

Based on the given information, we can determine that side DC is equal to 120 units and side DB is equal to 160 units. Since segment AC connects points A and C, and the figure does not provide any information about the length of side AB, we cannot determine the length of segment AC based on the given information. Therefore, the correct answer is "Cannot be determined."

Explanation

Based on the given information, we can determine that side DC is equal to 120 units and side DB is equal to 160 units. Since segment AC connects points A and C, and the figure does not provide any information about the length of side AB, we cannot determine the length of segment AC based on the given information. Therefore, the correct answer is "Cannot be determined."

6. Which of the following is not a criterion for congruence of triangles?

Side, Side, Side (SSS)

Angle Side Angle (ASA)

Side, Side , Angle (SSA)

Side, Angle, Side (SAS)

The criterion for congruence of triangles states that two triangles are congruent if they have the same corresponding angles and the lengths of their corresponding sides are equal. This is known as the Side, Side, Side (SSS) criterion. Angle Side Angle (ASA) states that two triangles are congruent if they have two corresponding angles and the included side equal. Side, Angle, Side (SAS) states that two triangles are congruent if they have two corresponding sides and the included angle equal. However, Side, Side, Angle (SSA) is not a criterion for congruence of triangles because two triangles can have two corresponding sides and a non-included angle equal, but still not be congruent.

Explanation

The criterion for congruence of triangles states that two triangles are congruent if they have the same corresponding angles and the lengths of their corresponding sides are equal. This is known as the Side, Side, Side (SSS) criterion. Angle Side Angle (ASA) states that two triangles are congruent if they have two corresponding angles and the included side equal. Side, Angle, Side (SAS) states that two triangles are congruent if they have two corresponding sides and the included angle equal. However, Side, Side, Angle (SSA) is not a criterion for congruence of triangles because two triangles can have two corresponding sides and a non-included angle equal, but still not be congruent.

7. Among two congruent angles one has measure 70, then the measure of other angle is_____

If two angles are congruent, it means they have the same measure. In this case, one angle has a measure of 70. Since the angles are congruent, the measure of the other angle must also be 70.

Explanation

If two angles are congruent, it means they have the same measure. In this case, one angle has a measure of 70. Since the angles are congruent, the measure of the other angle must also be 70.

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8. Look at the triangle ABC. O is the center. Which statement is always correct about triangle ABC?

Segments DF and AE are congruent.

Segments AE and EC are congruent.

Segments CD and BE are congruent.

Segments BO and OE are congruent

In a triangle with O as the center, the statement "Segments AE and EC are congruent" is always correct. This is because in a triangle, the line segment joining the center of the triangle to the midpoint of any side is always half the length of that side. Therefore, in triangle ABC, segment AE is congruent to segment EC.

Explanation

In a triangle with O as the center, the statement "Segments AE and EC are congruent" is always correct. This is because in a triangle, the line segment joining the center of the triangle to the midpoint of any side is always half the length of that side. Therefore, in triangle ABC, segment AE is congruent to segment EC.

9. Karabo has designed two triangular flower beds, as shown below. Which statement is true for the two flower beds?

The length of side PQ is equal to 10 feet.

They have the same perimeter.

They have different areas.

He length of side BC is equal to 10 feet.

The statement "They have the same perimeter" is true for the two flower beds because the perimeter of a triangle is the sum of the lengths of its sides. Since both flower beds have sides of equal length (10 feet), their perimeters would be equal.

Explanation

The statement "They have the same perimeter" is true for the two flower beds because the perimeter of a triangle is the sum of the lengths of its sides. Since both flower beds have sides of equal length (10 feet), their perimeters would be equal.

10. The triangles are similar, solve for the question mark.

21

12.5

18

15

The triangles are similar, which means that they have the same shape but possibly different sizes. To find the value of the question mark, we can set up a proportion using the corresponding sides of the triangles. By comparing the sides of the given triangles, we can see that the ratio of the length of the question mark side to the length of the 21 side is the same as the ratio of the length of the 18 side to the length of the 12.5 side. Solving this proportion, we find that the length of the question mark side is 18.

Explanation

The triangles are similar, which means that they have the same shape but possibly different sizes. To find the value of the question mark, we can set up a proportion using the corresponding sides of the triangles. By comparing the sides of the given triangles, we can see that the ratio of the length of the question mark side to the length of the 21 side is the same as the ratio of the length of the 18 side to the length of the 12.5 side. Solving this proportion, we find that the length of the question mark side is 18.

11. A triangle has sizes measuring 11 cm, 16 cm, and 16 cm. A similar triangle has sides measuring x cm, 24 cm, and 24 cm. What is x?

X = 19 cm

X = 16.5 cm

X = 24cm

X = 16 cm

The given triangle has two sides measuring 16 cm, which are equal in length. The similar triangle also has two sides measuring 24 cm, which are equal in length. Since the sides of similar triangles are proportional, we can set up a proportion to solve for x. The proportion is (11 cm)/(16 cm) = (x cm)/(24 cm). Cross multiplying gives us 11 cm * 24 cm = 16 cm * x cm. Solving for x gives us x = (11 cm * 24 cm) / 16 cm = 16.5 cm. Therefore, x = 16.5 cm is the correct answer.

Explanation

The given triangle has two sides measuring 16 cm, which are equal in length. The similar triangle also has two sides measuring 24 cm, which are equal in length. Since the sides of similar triangles are proportional, we can set up a proportion to solve for x. The proportion is (11 cm)/(16 cm) = (x cm)/(24 cm). Cross multiplying gives us 11 cm * 24 cm = 16 cm * x cm. Solving for x gives us x = (11 cm * 24 cm) / 16 cm = 16.5 cm. Therefore, x = 16.5 cm is the correct answer.

12. In each pair of triangles, parts are congruent as marked. Which pair of triangles are congruent by ASA?

Triangle pair 1

Triangle pair 2

Triangle pair 3

Triangle pair 4

not-available-via-ai

Explanation

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13. In the figure shown below, segment AM bisects angle BAC, and NC is drawn parallel to AM. Which triangle is similar to Triangle BAM?

Triangle MAC.

Triangle BNC.

Triangle BAC

Triangle ACN

Triangle BNC is similar to Triangle BAM because they have the same angle measures. Segment AM bisects angle BAC, so angle BAM is congruent to angle MAC. Since NC is drawn parallel to AM, angle BNC is congruent to angle MAC as well. Therefore, Triangle BNC is similar to Triangle BAM.

Explanation

Triangle BNC is similar to Triangle BAM because they have the same angle measures. Segment AM bisects angle BAC, so angle BAM is congruent to angle MAC. Since NC is drawn parallel to AM, angle BNC is congruent to angle MAC as well. Therefore, Triangle BNC is similar to Triangle BAM.

14. Solve for x, and y.

X = 12y = 60

X = 145y = 60

X = 144y = 60

X = 144y = 66

The given equations are a set of simultaneous equations. The first equation states that x is equal to 144, and the second equation states that y is equal to 60. These values satisfy all the given equations, making them the correct solution.

Explanation

The given equations are a set of simultaneous equations. The first equation states that x is equal to 144, and the second equation states that y is equal to 60. These values satisfy all the given equations, making them the correct solution.

15. Triangles are similar if:

All three pairs of corresponding sides are in the same proportion.

Two pairs of sides in the same proportion and the included angle equal.

They have the same shape, but cannot be different sizes.

All three pairs of corresponding angles are the same.

The correct answer is that triangles are similar if all three pairs of corresponding sides are in the same proportion, two pairs of sides are in the same proportion and the included angle is equal, and all three pairs of corresponding angles are the same. This means that for two triangles to be similar, their corresponding sides must be proportional in length, their corresponding angles must be equal, and if two pairs of sides are proportional in length, the included angle between them must also be equal.

Explanation

The correct answer is that triangles are similar if all three pairs of corresponding sides are in the same proportion, two pairs of sides are in the same proportion and the included angle is equal, and all three pairs of corresponding angles are the same. This means that for two triangles to be similar, their corresponding sides must be proportional in length, their corresponding angles must be equal, and if two pairs of sides are proportional in length, the included angle between them must also be equal.

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