Unit 6 Test Review: Part 1

In a right triangle, an altitude to the hypotenuse creates two smaller right triangles similar to the original. If the hypotenuse is split into segments of lengths 4 and 5 by the foot of the altitude, find the length of the altitude to the hypotenuse.

Tags

CCSS.HSG.SRT.B.4

In triangle ABC, right at D with AD = 8 and AC = 20, BD is an altitude from B to AC. Find BD.

Tags

CCSS.HSG.CO.C.10

In triangle ABC, right at C. Point D is on AB such that CD is an altitude. If AB = 12 and AC = 8, find AD.

Tags

CCSS.HSG.CO.C.10

Two right triangles share an altitude. The slanted left leg has length x, and the right small triangle has hypotenuse √14 and base √2. The base of the left large right triangle is 6√2. Find x.

Tags

CCSS.HSG.SRT.B.4

Find the ratio of 5 inches to 7 feet. Express your answer as a simplified fraction.

(a)  

Tags

CCSS.6.RP.A.1

CCSS.6.RP.A.2

Solve the proportion (x − 4)/6 = x/8 for x.

(a)  

Tags

CCSS.7.EE.B.4A

If 3x = 2y, find the ratio of x to y in simplest form.

(a)  

If ΔABC is similar to ΔPQR, then AC/AB equals which ratio of corresponding sides?

Tags

CCSS.HSG.SRT.A.2

Given triangles ΔPRQ ∼ ΔBAC with AB = 6, PR = 12, PQ = 9, and QR = 15. Find AC.

(a)  

Tags

CCSS.HSG.SRT.A.2

In the figure, a segment parallel to the triangle’s base splits the sides into proportional lengths. The left side is divided into lengths 5 and 2 (top then bottom), and the right side into lengths 6 and x (top then bottom). The mid-segment corresponding to the top portion has length 4, and the base has length y. Find x and y.

Tags

CCSS.HSG.SRT.B.4