O
Regents Road Map #5
Name:
Geometry Perio .
Directions: Work on al oblems assigned hese problems should be completed along with daily
ted per night. This assignment is subject to collection and
homework. One page shou
grading at any point. WORK MUST BE SHOWN FOR EVERY PROBLEM. When you receive this back check
your work online.
1. Line segment AB with endpoints A(4, 16) and B(20, 4) lies in the coordinate
plane. The segment will be dilated with a scale factor of 2 and a center at
the origin to
AB. What will be the length of A'B?
15
12
3
2. Construct a line perpendicular to the given line and
through point P.
ABCD is a parallelogram with diagonals AC and BD intersecting at E
Oegrtbe • single rig}d motion that maps LAED onto A CEB.
c
4. In the diagram below, right triangle RSU is inscribed in circle O, and UT is the altitude drawn to
hypotenuse RS. The length of RT is 16 more than the length of TS and IV— 15.
Find the length of TS.
IS
Find, in simplest radical form, the length of RU.
xso=x
5. The slope of QR is
and the slope of ST s —. If QRL ST, determine and state the value ofx.
6. For which diagram is the statemen
not always true??
4)
Explain your thinking,
Triangle A' B' c is
the image of AABCafter
a dilation
mZA =
on.
Which statement is true?
(mZA')
8. In the diagram of AABC
below, DE IlAB,
to
If
1) 10
4, CA 10, CE=I+2, and
41-7, what is the length of CE?
SFS
7-0k -20
=
. If two sides of a triangle have lengths of4 and 10, the third side could be
10. In isosceles trapezoid QRST shown below, QR and TSare bases.
If mZQ 5x+3 and mZR 'x
15, what is mZQ?
11. A circle whose center has coordinates (—3,4)passes through e origi
circle?
1) (x+3 2 +
—4
2)
-4
x +3 2 +
What is the equation of the
2 =25
= 25
51,
12. Given the theorem, "The sum of the measures of the interior angles of a triangle is 1800 " complete
the proof for this theorem.
c
D
Given: AABC
Prove: tnZ1 +
= 1800
Fill in the missing reasons below.
1
Statements
3
Reasons
(1) AABC
(1) Given
(2) Through point C, draw DCE parallel
(2)
(3)mZ1-—mZACD, mL3J= mZBCE
(3)
(4) mZACD + ma + mZBCE = 1800
add
(5) mZI + miZ2 + m 3 = 1800
IYO'