Congruent figures
Quadrilateral PQRS is congruent to quadrilateral WXYZ. Given: ∠P = 80°, ∠Q = 100°, ∠R = 90°c. Find the measures of all angles in quadrilateral WXYZ
∠W = 80°, ∠X = 100°, ∠Y = 90°, ∠Z = 90°
Triangle ABC is similar to triangle DEF. The sides of triangle ABC are 3 cm, 4 cm, and 5 cm. If the shortest side of triangle DEF is 6 cm, what are the lengths of the other two sides?
The shortest side of ABC is 3 cm.
Jake is designing a triangular flag. He makes a model where the sides measure 5 cm, 6 cm, and 7 cm.The real flag will be 3 times bigger in size but similar in shape.What will be the lengths of the sides of the real flag?
The sides of the real flag are 15 cm, 18 cm, and 21 cm
A soda can is shaped like a cylinder with a radius of 4 cm and height of 12 cm.What is the surface area of the can?
401.9 cm²
A dart is thrown randomly at a square dartboard that is 20 cm on each side. There is a circular bullseye in the center with a radius of 5 cm. What is the probability the dart hits the bullseye?
1/25
Two triangles, ΔABC and ΔDEF, have the following side lengths. AB = 6 cm, BC = 8 cm, AC = 10 cm DE = 6 cm, EF = 8 cm, DF = 10 cm. Which congruence postulate proves that ΔABC ≅ ΔDEF?
A) Angle-Side-Angle (ASA) B) Side-Side-Side (SSS) C) Side-Angle-Side (SAS) D) Angle-Angle-Side (AAS)
B) Side-Side-Side(SSS)
A 6-foot tall person casts a 4-foot shadow. At the same time, a tree casts a 12-foot shadow. How tall is the tree?
The tree is 18 feet tall
Triangle XYZ is similar to triangle ABC.In triangle XYZ, angle X = 40°, angle Y = 65°.What is the measure of angle Z in triangle XYZ?
Angle Z is 75°
A triangular prism has a triangular base with sides 3 cm, 4 cm, and 5 cm, and a height (length of the prism) of 10 cm.What is the surface area of the prism?
132 cm²
A point is chosen at random on a line segment that is 10 cm long. What is the probability that the point is within the first 4 cm of the segment?
A)1/2 B)1/3 C)1/4 D)1/6
B)1/3
Sarah is working on a geometry project involving triangle transformations. She draws triangle MNO with the following coordinates:M(2, 1), N(4, 1), and O(3, 4)She then rotates the triangle 90° counterclockwise about the origin to create a new triangle, which she labels PQR.What are the coordinates of triangle PQR after the rotation?
P = (–1, 2), Q = (–1, 4), R = (–4, 3)
Rectangle R has a length of 8 cm and a width of 5 cm.Rectangle S is similar to rectangle R and has a length of 12 cm.What is the width of rectangle S?
A. 6.5 cm B. 7 cm C. 7.5 cm D. 8 cm
C. 7.5
Two triangles are similar.In the smaller triangle, the sides are 4 cm, 6 cm, and 8 cm.In the larger triangle, the shortest side is labeled 2x, and the longest side is labeled 4x.What is the value of x?
x=2
A cereal box is shaped like a rectangular prism. It is 10 cm long, 6 cm wide, and 20 cm tall. What is the surface area of the box?
760 cm²