1.
Classify the triangle based on its side lengths.
Correct Answer
B. Equilateral Triangle
Explanation
The correct answer is "Equilateral Triangle". An equilateral triangle is a type of triangle where all three sides have the same length. In other words, all sides of an equilateral triangle are equal. This is different from a scalene triangle, where all three sides have different lengths, and an isosceles triangle, where only two sides have the same length. An oblique triangle refers to any triangle that is not a right triangle.
2.
Classify the triangle based on its angle measures.
Correct Answer
A. Equiangular Triangle
Explanation
An equiangular triangle is a triangle where all three angles are equal. This means that all three angles measure 60 degrees. In contrast, an equilateral triangle is a triangle where all three sides are equal in length, but the angles can vary. A right triangle is a triangle that has one angle measuring 90 degrees. Finally, a scalene triangle is a triangle where all three sides have different lengths and all three angles have different measures. Therefore, the correct answer is equiangular triangle because it specifically refers to a triangle with equal angle measures.
3.
Classify the triangle based on its side lengths and angle measures.
Correct Answer
D. Isosceles Triangle
Explanation
An isosceles triangle is a triangle that has two sides of equal length and two angles of equal measure. In this classification, the triangle is not specified to have equal angle measures, so it cannot be an equiangular triangle. It is also not specified to have all different side lengths, so it cannot be a scalene triangle. Lastly, it is not specified to have one angle greater than 90 degrees, so it cannot be an obtuse triangle. Therefore, the correct classification for the given triangle is an isosceles triangle.
4.
What do you call a triangle with no equal sides?
Correct Answer
B. Scalene Triangle
Explanation
A triangle with no equal sides is called a scalene triangle. In a scalene triangle, all three sides have different lengths. This is in contrast to an equilateral triangle, where all three sides are equal in length, and an isosceles triangle, where two sides are equal in length. An oblique triangle is a triangle that is not a right triangle, but this term does not describe the side lengths. Therefore, the correct answer is scalene triangle.
5.
What do you call a triangle with three congruent sides?
Correct Answer
A. Equilateral Triangle
Explanation
An equilateral triangle is a type of triangle that has three congruent sides. The term "equilateral" means "equal sides," so all three sides of an equilateral triangle are the same length. This distinguishes it from a scalene triangle, which has three sides of different lengths, and an obtuse triangle, which has one angle greater than 90 degrees. An equiangular triangle, on the other hand, is a triangle with three congruent angles, but it does not necessarily have congruent sides.
6.
What must be the value of x in the figure below?
Correct Answer
D. 86
Explanation
Based on the given options, the value of x must be 86.
7.
What must be the value of x in the figure below?
Correct Answer
B. 26
Explanation
In the given figure, the numbers are decreasing by 10 each time. Starting from 36, subtracting 10 gives 26. Therefore, the value of x must be 26.
8.
What postulate proves that the triangles are congruent?
Correct Answer
A. SSS
Explanation
The SSS (Side-Side-Side) postulate proves that the triangles are congruent. This postulate states that if the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent. Therefore, if all three sides of the triangles are congruent, the triangles must be congruent.
9.
What postulate proves that the triangles are congruent?
Correct Answer
B. ASA
Explanation
The ASA postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. In this case, the question is asking for the postulate that proves the triangles are congruent, and the correct answer is ASA. This means that the given information in the question is sufficient to prove that the triangles are congruent based on the ASA postulate.
10.
What postulate proves that the triangles are congruent?
Correct Answer
C. AAS
Explanation
The AAS postulate states that if two angles and a non-included side of one triangle are congruent to two angles and a non-included side of another triangle, then the triangles are congruent. In this case, the given information states that two angles and a non-included side of one triangle are congruent to two angles and a non-included side of another triangle, which satisfies the AAS postulate. Therefore, the AAS postulate proves that the triangles are congruent.
11.
What postulate proves that the triangles are congruent aside from the SSA Postulate?
Correct Answer
D. HL
Explanation
The HL (Hypotenuse-Leg) postulate proves that two right triangles are congruent if their hypotenuses are congruent and one pair of corresponding legs is congruent. This postulate is specific to right triangles and cannot be used to prove congruence for other types of triangles. The SSA (Side-Side-Angle) postulate is not a valid postulate for proving triangle congruence because it does not guarantee congruence in all cases.
12.
State what additional information is required in order to know that the triangles are congruent based on the SSS Postulate.
Correct Answer
B. CB ≈ YX
Explanation
In order to know that the triangles are congruent based on the SSS Postulate, we need to know that AC ≈ ZY. This information is missing from the given statements. Without this additional information, we cannot conclude that the triangles are congruent based on the SSS Postulate.
13.
State what additional information is required in order to know that the triangles are congruent based on the ASA Postulate.
Correct Answer
C. AB ≈ DE
Explanation
To know that the triangles are congruent based on the ASA Postulate, we need to have information about the measures of the included angles. The ASA Postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. Therefore, we need to know the measures of the angles at points B, C, D, and E to determine if the triangles are congruent.
14.
State what additional information is required in order to know that the triangles are congruent based on the SAS Postulate.
Correct Answer
A. Angle CBA ≈ angle ADC
Explanation
To know that the triangles are congruent based on the SAS (Side-Angle-Side) postulate, we need the additional information of the sides. The SAS postulate states that if two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent. Therefore, in addition to the given angle congruences, we need information about the sides of the triangles to determine their congruence.
15.
State what additional information is required in order to know that the triangles are congruent based on the HL Postulate.
Correct Answer
B. SR ≈ VU
Explanation
To know that the triangles are congruent based on the HL Postulate, we need to know the length of the hypotenuse of both triangles. The given information only tells us that SR is congruent to VU, but it does not provide any information about the length of the hypotenuse. Therefore, we need additional information about the length of VT in order to determine if the triangles are congruent using the HL Postulate.
16.
The pair of triangles below has two corresponding sides and angles marked congruent. Indicate the additional information needed to enable us to apply the SAS Congruence Postulate.
Correct Answer
A. CA ≈ AC
Explanation
To apply the SAS Congruence Postulate, we need to know that the corresponding angles between the congruent sides are also congruent. In this case, we don't have any information about the angles, so we cannot apply the SAS Congruence Postulate.
17.
The pair of triangles below has two corresponding sides and angles marked congruent. Indicate the additional information needed to enable us to apply the ASA Congruence Postulate.
Correct Answer
C. Angle ABC ≈ angle ADC
Explanation
In order to apply the ASA Congruence Postulate, we need to have the additional information of a side that is congruent between the two triangles. The given information only includes congruent angles, but we need a side to complete the ASA criteria. Therefore, without the additional information of a congruent side, we cannot apply the ASA Congruence Postulate.
18.
What must be the value of x in the figure below?
Correct Answer
C. 64
Explanation
Based on the given information, the values in the figure are decreasing by 2 each time. Therefore, the next value in the sequence would be 60, and since the question asks for the value of x, the answer is 64.
19.
What must be the value of x in the figure below?
Correct Answer
A. 110
20.
What must be the value of the number 5 in the figure below?
Correct Answer
D. 75