Triangle Congruence: SSS and HL — Cumulative exam Answers

Circle R is shown. Tangents F G and H G intersect at point G outside of the circle to form an angle with a measure of 50 degrees. Point E is on the second arc. Arc F H has a measure of x degrees.

Derek Jeter challenges Albert Pujols to a batting battle. Each will earn 1 point for a hit other than a home run and 4 points for a home run in each round. Which player should you back given the statistics in the table below? Note that home runs are included as hits in the table.Data for Two BattersBatterAt BatsHitsHome RunsJeter4881569Pujols44812526

Miguel Cabrera has had 369 at bats, and he has 127 hits and 21 home runs. (Note: The home runs are included in the hits data.) If he is challenged to a batting battle, what is the expected score of each at bat if he earns 1 point for each hit that is not a home run and 5 points for each home run?

Triangle J K L is shown. Angle K L J is a right angle. The length of hypotenuse K J is 10.9 centimeters and the length of L J is 8.9 centimeters. Angle L K J is x.

Consider the following sets.U = {all triangles}E = {x|x ∈ U and x is equilateral}I = {x|x ∈ U and x is isosceles}S = {x|x ∈ U and x is scalene}A = {x|x ∈ U and x is acute}O = {x|x ∈ U and x is obtuse}R = {x|x ∈ U and x is right}Which is a subset of I?

A theater production group is making frames to support wall-like props. Three-foot beams form right triangles with 10-foot beams to allow them to stand, as shown in the image.

A beach has two floating docks. One is 650 meters east of the lifeguard stand. The other is 60° southeast and 750 meters from the lifeguard stand.Law of cosines:

is tangent to circle P at point Q.

Which best describes independent events?

The law of cosines is used to find the value of m.

Triangle A B C is shown. Angle B C A is a right angle. The length of hypotenuse A B is 20 centimeters and the length of B C is 10.5 centimeters. Angle A B C is x.

Circle B is inside of circle A.

A triangular prism with a rectangular base is stacked on top of a rectangular prism. The rectangle has side lengths of 20 and 15 units. The rectangular prism has a height of 12. The triangular prism has a height of 16 units.

Liliana is making a vase with a circular base. She wants the area of the base to be between 135 cm2 and 155 cm2.Which circle could represent the base of the vase? Use 3.14 for .

Circle Y is shown. Chords R T and S U intersect. Arc R S is 106 degrees. The angle that intercepts arc R S is 94 degrees.

A garden is designed in the shape of a rhombus formed from 4 identical 30°-60°-90° triangles. The shorter distance across the middle of the garden measures 30 feet.

To support a tree damaged in a storm, a 12-foot wire is secured from the ground to the tree at a point 10 feet off the ground. The tree meets the ground at a right angle.

Angle G is a circumscribed angle of circle E.

An oblique cylinder has a radius of 10 units and slant length of 26 units.

Belleville High School offers classes on three different foreign languages. Let A be the event that a student is in eleventh grade, and let B be the event that a student is enrolled in French class.