Download Unit 6: Proving Triangles Congruent

Geometry/PAP Geometry
End-of-Semester Review 2011
Unit 6: Proving Triangles Congruent
Basic concepts:
a. Congruent triangle theorems: SSS, SAS, ASA, AAS, and HL.
b. Corresponding parts of congruent triangles are congruent: CPCTC
c. Congruent triangles have exactly the same size and shape. One is a copy of the other.
1. ΔABC and ΔDOG are shown below.
What additional information would be
sufficient to prove ΔABC  ΔZBY by SAS?
A
Z
y
_____________________
C
Y
2. ΔCAT and ΔBAT are shown below.
What additional information would be
sufficient to prove ΔCAT  ΔBAT by AAS?
_____________________
C
T
A
B
3. If ΔBYD  ΔGRL by HL, then what would
have to be true about the two triangles?
Sketch ΔBYD and ΔGRL showing how they
could be congruent by HL.
_______________________________________
_______________________________________
_______________________________________
4. If ΔGRN  ΔYLW, segment GN  YL. TRUE/FLASE
EXPLAIN: _______________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
Unit 5: Similar Triangles and Propostion
Basic concepts:
a. Similar triangle theorems: AA~, SSS~, SAS~.
b. In similar triangles, all angles are congruent, and corresponding sides of the two
triangles are proportional.
c. In similar triangles, the proportion/scale factor is the same for every pair of
corresponding sides.
d. Use proportions to determine scale factor and missing information.
e. Similar figures have same shape, but not the same size. One is a dilation of the other.
1. The length of a model train is 18 inches.
It is a scale model of a train that is 48 feet
long. Use a ratio to determine the scale
factor.
Show work here.
2. A steel sculpture has been designed for the
lawn of the City Arts Building. One end of
the design looks like the sketch below. How
tall will the steel column on the right need to
be? Give the final answer in feet and inches.
Show work here.
20’ 3”
18 ‘
16 ‘
3. The ratio of the sides of a triangle is 8:15:17.
If the perimeter of the triangle is 480 inches,
find the length of each side of the triangle.
short side = __________
medium side = __________
long side = __________
Show work here.
4. Use proportions to solve for x.
12
x
Show work here.
6
8
x = __________
5. Use proportions to solve for x.
Show work here.
x
7.5
12
18
x = __________
6. Use proportions to solve for v.
7. The streets 7th Avenue, 8th Avenue, and 9th Show work here.
Avenue are parallel. They all intersect Laurel
Canyon Drive and Mountain Way Boulevard.
If all these streets are straight line segments,
how long is Laurel Canyon Drive between
7th Avenue and 9th Avenue?
A. 2101.7 ft
B. 2145 ft
C. 3921.7 ft
D. 4436 ft
8. A park ranger needs to find the location from
a helicopter of an injured bear. He knows
some of the trail distances, but needs to know
the horizontal distance from the peak of the
mountain. Find that distance.
30
ft
x
80 ft
48 ft
Show work here.
9. Use a proportion to
Solve for x.
Determine the length
of each of the given
segments.
3x
Show work here.
12
x
x+2
x = __________
3x = __________
x + 2 = __________
10. Prove that the two parallelograms are similar or
not similar. If similar, write the similarity
statement that describes the relationship between
the two figures. If the figures are not similar,
write a sentence that explains why they are not.
X
H
108
27
48
192
Y
W
F
G
108
27
48
192
Z
I
Proof of similarity.
11.
12.
If similar, write a similarity statement.
_________________________________
If not similar, write a sentence explaining.
_________________________________________
_________________________________________
w = ________
y = _________
60˚
14 2
w
6
3
12 3
13.
14.
y = _________
y
y = _________
y
6 3
30˚
45˚
56
15. Solve for x.
Show work here.
x
4
x
12
3
16.
Show work here.
y
2y - 5
x
x+3
3
4
17.
Show work here.
3x
5x
8x
60
18. The ratio of two complementary angles is
7 : 11. Find the measure of each angle.
19. The ratio of angles in a triangle is 1 : 2: 6. Find
the measure of each angle.
20. The ratio of two supplementary angles is 5 : 7.
Find the measure of the smaller angle.
Show work here.
smaller angle = __________
larger angle = ___________
Show work here.
smaller angle = __________
medium angle = _________
larger angle = ___________
Show work here.
smaller angle = __________