Lesson 4.1 To 4.3 Quiz

1) Given triangle ABC= triangle FGH, which angle is congruent to angle B?

Angle G

Angle F

Angle H

In a congruent triangle, corresponding angles are equal. Since triangle ABC is congruent to triangle FGH, angle B in triangle ABC is congruent to angle G in triangle FGH.

Explanation

In a congruent triangle, corresponding angles are equal. Since triangle ABC is congruent to triangle FGH, angle B in triangle ABC is congruent to angle G in triangle FGH.

2) Assume triangle DEF = triangle XYZ. IF DE = 14, DF = 15, and EF = 9, what is the length of XY?

14

15

9

If triangle DEF is congruent to triangle XYZ, it means that they have the same shape and size. Therefore, corresponding sides of the triangles are equal. Given that DE = 14, it implies that XY, which corresponds to DE, is also equal to 14.

Explanation

If triangle DEF is congruent to triangle XYZ, it means that they have the same shape and size. Therefore, corresponding sides of the triangles are equal. Given that DE = 14, it implies that XY, which corresponds to DE, is also equal to 14.

3) What is the missing angle?

133

47

43

The missing angle can be determined by subtracting the given angles from 180 degrees, since the sum of the angles in a triangle is always 180 degrees. Therefore, 180 - 133 - 43 = 4. Since the missing angle is less than 180 degrees, it must be positive. Thus, the missing angle is 47 degrees.

Explanation

The missing angle can be determined by subtracting the given angles from 180 degrees, since the sum of the angles in a triangle is always 180 degrees. Therefore, 180 - 133 - 43 = 4. Since the missing angle is less than 180 degrees, it must be positive. Thus, the missing angle is 47 degrees.

4) What is x?

85

95

15

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Explanation

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5) What is x?

35

55

125

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Explanation

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6) If triangle ABC = triangle JLK, what side is congruent to AB

JK

KL

JL

If triangle ABC is congruent to triangle JLK, it means that they have the same shape and size. Therefore, the corresponding sides of these triangles are congruent. Since AB is a side of triangle ABC, the corresponding side in triangle JLK that is congruent to AB is JL.

Explanation

If triangle ABC is congruent to triangle JLK, it means that they have the same shape and size. Therefore, the corresponding sides of these triangles are congruent. Since AB is a side of triangle ABC, the corresponding side in triangle JLK that is congruent to AB is JL.

7) What is x?

86

94

55

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Explanation

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8) How many angles are congruent in an equiangular triangle?

0

2

3

In an equiangular triangle, all three angles are congruent, meaning they have the same measure. Therefore, the correct answer is 3, as there are three congruent angles in an equiangular triangle.

Explanation

In an equiangular triangle, all three angles are congruent, meaning they have the same measure. Therefore, the correct answer is 3, as there are three congruent angles in an equiangular triangle.

9) What is x?

20

90

30

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Explanation

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10) What congruence postulate can be used to prove that the two triangles are congruent?

SSS

ASA

SAS

The congruence postulate that can be used to prove that the two triangles are congruent is SAS (Side-Angle-Side). This postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. In this case, the given information is that one side and the two angles of one triangle are congruent to one side and the two angles of another triangle, satisfying the conditions of the SAS postulate. Therefore, the triangles can be proven to be congruent using the SAS postulate.

Explanation

The congruence postulate that can be used to prove that the two triangles are congruent is SAS (Side-Angle-Side). This postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. In this case, the given information is that one side and the two angles of one triangle are congruent to one side and the two angles of another triangle, satisfying the conditions of the SAS postulate. Therefore, the triangles can be proven to be congruent using the SAS postulate.

11) What is y?

160

20

80

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Explanation

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12) How many sides are congruent in a scalene triangle?

0

2

3

A scalene triangle is a triangle that has three sides of different lengths. Since congruent sides are sides that have the same length, a scalene triangle does not have any congruent sides. Therefore, the correct answer is 0.

Explanation

A scalene triangle is a triangle that has three sides of different lengths. Since congruent sides are sides that have the same length, a scalene triangle does not have any congruent sides. Therefore, the correct answer is 0.

13) You can build two triangles that have the same side lengths but are not congruent.

True

False

Two triangles with the same side lengths are always congruent. This is because the side lengths determine the shape and size of a triangle. If two triangles have the same side lengths, then all corresponding angles will also be equal, making them congruent. Therefore, the statement that two triangles with the same side lengths are not congruent is false.

Explanation

Two triangles with the same side lengths are always congruent. This is because the side lengths determine the shape and size of a triangle. If two triangles have the same side lengths, then all corresponding angles will also be equal, making them congruent. Therefore, the statement that two triangles with the same side lengths are not congruent is false.

14) What is x?

42

48

142

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Explanation

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15) How would you classify this triangle? (Choose all that apply)

Scalene

Isosceles

Acute

Right

Equilateral

This triangle can be classified as scalene because it has three sides of different lengths. It can also be classified as acute because all of its angles are less than 90 degrees.

Explanation

This triangle can be classified as scalene because it has three sides of different lengths. It can also be classified as acute because all of its angles are less than 90 degrees.

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16) How would you classify this triangle?(Check all that apply)

Scalene

Right

Isosceles

Acute

Equlateral

The triangle can be classified as a right triangle because it has one angle that measures 90 degrees. It can also be classified as an isosceles triangle because it has two sides that are equal in length.

Explanation

The triangle can be classified as a right triangle because it has one angle that measures 90 degrees. It can also be classified as an isosceles triangle because it has two sides that are equal in length.

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17) Extra Credit:All equilateral triangles are also isosceles trianlges

True

False

An isosceles triangle has AT LEAST two congruent sides. An equilateral triangle has three congruent sides, which means that it has at least two sides congruent.

Explanation

An isosceles triangle has AT LEAST two congruent sides. An equilateral triangle has three congruent sides, which means that it has at least two sides congruent.