Name:_____________________________________________
Right Triangle Review Sheet
Date:________________ Period:________
Geometry Honors
Directions: Answer the following questions completely on a separate sheet of paper.
Part One: Simplify the following radicals.
1)
2)
3)
6)
7)
8)
4)
5)
9)
10)
Part Two: Add/Subtract the following radicals. (Answers in simplest radical form)
1)
2)
3)
4)
5)
6)
Part Three: Multiply/Divide the following radicals. (Answers in simplest radical form)
1)
2)
3)
4)
5)
6)
7)
8)
Part Four: Word problems and radicals.
1) The length of a rectangle is
and the width is
. Express each answer in simplest radical form:
a. Find the area of the rectangle.
b. Find the perimeter of the rectangle.
2) If a square has a side of
, what is the area and perimeter in simplest radical form?
3) Express the area of the figure in simplest radical form if the height is
4) The area of a rectangle is
5) If the perimeter of a rectangle is
and the length is
inches and the base is
, what is the width?
and the length is
, what is the width?
6) Find the area and perimeter of the following examples. Answers should be in simplest radical form.
a.
b.
.
Part Five: Pythagorean Theorem/Altitude Rule/Leg Rule
1) The lengths of the sides of a triangle are 6, 2.5, and 15. Is this a right triangle?
2) In the diagram below of right triangle ABC, altitude
is drawn to hypotenuse
What is the length of
?
(1)
(2)
(3)
(4) 1
, AC=16, and CD=7.
3) The lengths of the sides of a triangle are .9, 4, and 4.1. Is this a right triangle?
4) Find the measure of the diagonal of a rectangle whose sides are 25 and 50, in simplest radical form.
5) In the diagram below of right triangle ACB, altitude
is drawn to hypotenuse
If AB = 36 and AC = 12, what is the length of
?
(1) 32
(2) 6
(3) 3
(4) 4
.
6) Firefighters have a 29 foot extension ladder in order to reach 25 feet up the building. How far away
from the building should the ladder be placed? Round to the nearest tenth. Include a diagram with your
answer.
7) What is the exact length of the diagonal of a square with a perimeter of 60 inches? (in simplest radical
form).
8) Given the following diagram, find the length of a, b, and c. Round answers to the nearest tenth.
9) Use the diagram below to find the value of x. Answer must be in simplest radical form.
10) Two joggers run 8 miles north and 5 miles west. What is the shortest distance, to the nearest mile,
they must travel to return to the starting point?
11) In right triangle JKL, <K is a right angle. Altitude KH intersects the hypotenuse JL in such a way JH is 21
more than the length of HL.
a. If HL = x, then find the value of JH in terms of x.
b. If the altitude, KH = 10, then what is the value of HL.
12) A right triangle has a leg with a length of 5 and a hypotenuse with the length of
length of the other leg?
Part Six: Special Right Triangles
For questions 1-8, find the exact value of x and y.
1)
2)
3)
5)
6)
7)
. What is the
4)
8)
9) The length of the hypotenuse of a 30-60-90 triangle is 20 inches. What is the length of the shorter leg?
10) A ladder leaning against a wall makes an angle of 60 degrees with the ground. The base of the ladder is
3 ft from the building. How high above the ground is the top of the ladder?
11) Find the length of the leg of a right triangle if one angle measures 45 degrees and the hypotenuse is 16
inches.
12) Find the exact value of w and y.
Name:_____________________________________________
Review Sheet
Date:________________ Period:________
Geometry Honors
Directions: Answer the following questions completely on a separate sheet of paper.
1) What is the equation of the line passing through the point (-8,1) and is parallel to the line whose equation is
?
2)
3)
4)
5)
6) In
,
and
. If the shortest side of similar
is 12, what are the measures of the
remaining two sides? What is the perimeter of
? Include a diagram with your answer.
7) In
shown below, L is the midpoint of , M is the midpoint of
and
, find the perimeter of trapezoid
.
, and N is the midpoint of
. If
8) Triangle CAT has coordinates C(-6,-3), A(-1,-3), T(-2,-1). The images of triangle CAT after composition
is triangle C”A”T”. State and label the coordinates of C”A”T”.
9)
10)
11) Construct equilateral triangle ABC. Leave all
construction marks.
A
B
12)
Review Sheet:
Part I:
1.)
2.)
3.)
4.)
5.)
6.)
7.)
8.)
9.)
10.)
2.)
3.)
4.)
5.)
1.)
2.)
3.) -144
4.) 17
5.)
6.) 15
7.)
8.)
4.) w = 25
5.)
Part II:
1.)
6.)
Part III:
Part IV:
1.) a) 144
b.)
6.) a)
;
2.)
; A = 20
3.)
b) A = 96;
Part V:
1.) no
2.) (1)
8.) a = 4.6, b = 11.1, c = 1.9
3.) yes
4.)
5.) (4)
6.) 14.7
9.)
10.) 9
11.) a) x + 21 b) 4
7.)
12.) 10
Part VI:
1.)
2.)
3.)
4.)
5.)
6.)
7.)
8.)
9.) 10
11.)
12.) w = 9;
Review Questions:
1.)
7.) 34
12.) AC
2.) & 3.) correct proof
8.) C”(10,-2) A”(5,-2) T”(6,-4)
4.) 5
5.) (2)
6.) 32 & 40
9.) (3)
10.) (1)
11.) correct construction