MYA 2024 Review 1

Read the argument and justification. Then select the correct answer.

"In an isosceles triangle 𝐴𝐵𝐶 with 𝐴𝐶≅𝐴𝐵, if 𝑚∠𝐵=50° then 𝑚∠𝐶=40°".

• The argument is valid, the angles opposite to the congruent sides of an isosceles triangle are complementary.

• The argument is invalid, the angles opposite to the congruent sides of an isosceles triangle are supplementary.

• The argument is invalid, the angles opposite to the congruent sides of an isosceles triangle are congruent.

• The argument is invalid, the angles opposite to the congruent sides of an isosceles triangle are corresponding.

Point B is located on line segment. Point A is located at (-3, 6) and point B is located at (n, q) and point C is located at (-3, -1). The ratio of AB:AC is 2/5. What are the values of n and q?

• (-3,-1)

• (-3,5)

• (-3, 0)

• (-3, 2)

The vertices of Δ𝐴𝐵𝐶 are A(7, 3), B(-8, 6), C(0, -5). If Δ𝐴𝐵𝐶 is transformed following the rule (𝑥, 𝑦)→(𝑥−9, 𝑦+5), what are the coordinates of the vertices of Δ𝐴′𝐵′𝐶′ ?

• A. A'(-2, 8), B'(-17, 11), C'(-9, 0)

• B. A'(8, -2), B'(11, -17), C'(0, -9)

• C. A'(12, -6), B'(-3, -3), C'(5, -14)

• D. A'(16, -2), B'(1, 1), C'(9, -10)

Read the statement. 'If two sides and the included angle of a triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.' Which sentence is the inverse of the statement shown?

• A. If two triangles are congruent, then the two sides and the included angle of a triangle are congruent to two sides and the included angle of another triangle.

• B. If two sides and the included angle of a triangle are congruent to two sides and the included angle of another triangle, then the two triangles are not congruent.

• C. If two sides and the included angle of a triangle are not congruent to two sides and the included angle of another triangle, then the two triangles are not congruent.

• D. If two triangles are not congruent, then the two sides and the included angle of a triangle are not congruent to two sides and the included angle of another triangle.

In the figure shown, 𝑎∥𝑏 and 𝑐∥𝑑.

What are the values of X and Y?

• X=14

  Y=20

• X=14

  Y=60

• X=40

  Y=10

• X=25

  Y=40

Triangles RST and XYZ are shown below. Malik knows that ∠R≅ ∠X and ∠T≅ ∠Z. He claims that triangles RST and XYZ are congruent. As part of her reasoning, which criterion could she use? Select all that apply.

• A. Angle-Angle (AA)

• B. Hypotenuse-Leg (HL)

• C. Side-Angle-Side (SAS)

• D. Angle-Side-Angle (ASA)

• E. Side-Side-Side (SSS)

Susanne is creating a triangular birthday card for her teacher. In order to glue lace around the outside of the card, She needs to know the length of each side. She knows that two of the sides measure 4 inches and 9 inches. If the length of the third side is 𝑥 inches, which inequality is true?

• A. 5≤𝑥≤13

• B. 5<𝑥<13

• C. ≤𝑥<36

• D. <𝑥<36

A square is plotted on a coordinate plane. Henry claims that any transformation on the square will preserve the length of its sides. Which of the following transformations could be used to show that Henry's claim is incorrect? Select all that apply.

• A. translation of 5 units to the right

• B. horizontal stretch by a factor of 1/3

• C. dilation by a factor of 2 through the origin

• D. rotation of 45° clockwise about the square's center E. a reflection over the x-axis.

The graph of a triangle is shown. Which graphs show the median from each vertex of the triangle to find the centroid? A B C D

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If ΔABC, with coordinates A(2, -1), B(4, -1), C(2, -3), is reflected over the line 𝑦=𝑥, what are the coordinates of ΔA'B'C'?

• A. A'(2, 1), B'(4, 1), C'(2, 3)

• B. A'(-1, 2), B'(-1, 4), C'(-3, 2)

• C. A'(-2, 1), B'(-4, 1), C'(-2, 3)

• D. A'(-2, -1), B'(-4, -1), C'(-2, -3)