Isosceles Triangles — Cumulative exam Answers

Ricardo has a square hot tub. He wants to build a square pool next to it that is a dilation of the hot tub using a scale factor of 5.

Given: a ∥ b and ∠1 ≅ ∠3Prove: e ∥ fWe know that angle 1 is congruent to angle 3 and that line a is parallel to line b because they are given. We see that __________ by the alternate exterior angles theorem. Therefore, angle 2 is congruent to angle 3 by the transitive property. So, we can conclude that lines e and f are parallel by the converse alternate exterior angles theorem.Which information is missing in the paragraph proof?

Which distance measures 5 units?

Triangle EFG is transformed to create triangle E'F'G'.

Triangle N L M is reflected over a line to form triangle A B C.

Triangles R S T and V U T are connected at point T.

Triangles C B A and R Q P are shown. The length of C B is 10, the length of B A is 10, and the length of A C is 14. The length of R Q is y, the length of Q P is 6, and the length of P R is 28.

Rhombus L M N O is shown. Diagonals are drawn from point L to point N and from point M to point O and intersect at point P. The length of L M is 3 x minus 3 and the length of M N is x + 7.

Triangle A B C is cut by line segment S T. Line segment S T goes from side A B to side C B. Lines S T and A C are parallel. The length of S B is 10 feet, the length of B T is 9 feet, and the length of C T is 2.7 feet.

Consider the diagram.

Pentagon ABCDE is dilated according to the ruleDO,3(x,y) to create the image pentagon A'B'C'D'E', which is shown on the graph.

The rule is applied to ΔBCD to produce ΔB"C"D". Point B" of the final image is at (–4, 1).

On a coordinate plane, 2 triangles are shown. Triangle L M N has points (negative 1, 3), (3, 1), and (negative 1, 1). Triangle L prime M prime N prime has points (negative 2, negative 1), (6, negative 5), and (negative 2, negative 5).

Which statements must be true about the two congruent, shaded figures? Select two options.

Angle KLM and angle MLN are a linear pair.

Parallelogram L M N O is shown. Angle N is (5 x) degrees and angle L is (3 x + 40) degrees.

Given that D is the midpoint of AB and B is the midpoint of AC, which statement must be true?

Planes A and B intersect.

One exterior angle of a regular pentagon has a measure of (2x)°. What is the value of x?

On a coordinate plane, 3 triangles are shown. Triangle A B C has points (5, 2), (2, 4), (2, 1). Triangle A prime B prime C prime has points (negative 2, 5), (negative 4, 2), (negative 1, 2). Triangle A double-prime B double-prime C double-prime has points (negative 2, negative 5), (negative 4, negative 2), (negative 1, negative 2).