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Brooklyn Technical High School
Review #3 MP1 (Answers)
Geometry Term I
Name ____________________________
Instructor: Mr. Rodriguez Period ____________________________
̅̅̅̅ ≅ ̅̅̅̅
1) In isosceles ΔABC, 𝑨𝑩
𝑩𝑪, 𝒎 < 𝑨 = 𝒙 + 𝟏𝟎, and 𝒎 < 𝑪 = 𝟐𝒙 − 𝟐𝟎. Find 𝒎 < 𝑨.
A) 10
B) 20
C) 30
D) 40
E) 50
B
A
C
Good problem solving technique here is to draw a diagram.
Since two sides of the triangle are congruent, the angles opposite
those sides are congruent, namely angle 𝐴 and angle 𝐶. Set those
two equal to each other; 𝑥 + 10 = 2𝑥 − 20. Solve for 𝑥 and you
get 𝑥 = 30. Substitute back into the expression for A;
𝑚 < 𝐴 = 30 + 10 = 40.
Ans
.
D) 40
2) Which of the following may be the length of the sides of a triangle?
A) 4, 9, 13 B) 5, 8, 12
C) 5, 5, 13
D) 5, 5, 10
E) 8, 3, 2
The sum of any two sides of a triangle has to be
more than the third side. For choice B, any two
numbers you pick, the sum will be greater than the
third number.
Ans.
B) 5, 8, 12
3) If two angles are supplementary and congruent, then they are
A) acute angles
B) obtuse angles
C) right angles
D) vertical angles
E) isosceles angles
If two angles are supplementary , the sum of the
two angles is 180. If the angles are congruent, then
each angle is 90. A 90o is a right angle.
4) If a conditional statement is true, which statement is also true?
A) inverse
B) converse
C) contrapositive D) negation
Ans.
C) Right Angles
E) conjunction
Ans
.
C) Contrapositive
A conditional statement p q is has the same truth value
(logically equivalent) as its contrapositive ~q  ~p
5) Which is a possible length for the third side of a triangle whose other two sides are 10 and 18?
A) 5
B) 8
C) 28
D) 35 E) 19
The measure of the third side of a triangle is greater than the difference between the two sides and the
sum of the two sides or 𝑎 – 𝑏 < 𝑡ℎ𝑖𝑟𝑑 𝑠𝑖𝑑𝑒 < 𝑎 + 𝑏 (where a > b).
(18 − 10) < 𝑡ℎ𝑖𝑟𝑑 𝑠𝑖𝑑𝑒 > (18 + 10)  8 < 𝑡ℎ𝑖𝑟𝑑 𝑠𝑖𝑑𝑒 < 28. Third side could be 19.
Ans
.
E)19
6) What must be true before using CPCTC in a proof?
A) Two triangles similar
B) Two triangles congruent
C) All angles congruent D) Reflexive property
Ans
E) AA
CPCTC represents “Corresponding Parts of Congruent Triangles are
.
B
Congruent” To use this we need congruent triangles.
7) The orthocenter is on which segment?
A) Altitude
B) Median
C) Base
D) Angle Bisector
E) Hypotenuse
The orthocenter is the intersection of the 3 altitudes of a triangle. Therefore the
orthocenter will be on one of the altitudes of the triangle
8) In the figure at right, lines 𝑘 𝑎𝑛𝑑 𝑚 intersect at point A,
𝑚 < 1 = (3𝑛 + 14)o, and 𝑚 < 3 = (36𝑛 + 3)o, find 𝑚 < 2.
A) 4o
B) 33o
C) 57o
D) 147o
E) 165o
<1 and <2 are vertical angles. Vertical angles are congruent. Set < 1 equal to angle
2, or (3𝑛 + 14) = (36𝑛 + 3). Solving for 𝑛 gives us 1⁄3. Substituting for 𝑛 gives
us 15 for 𝑚 < 1 which is supplementary to 2 making < 2 = 1650
Ans
.
A)
k
m
A
1
3 2
Ans
.
E) 165
9) In 𝛥𝑅𝑆𝑇, 𝑅𝑆 = 9, 𝑆𝑇 = 9, 𝑎𝑛𝑑 𝑇𝑅 = 11. Which angle of 𝛥𝑅𝑆𝑇, has the greatest measure?
A) < 𝑅
B) < 𝑆
C) < 𝑇
D) < 𝑅 𝑎𝑛𝑑 < 𝑇
E) Can’t be determined
The largest angle is opposite the
longest side. <S is opposite the
longest side.
S
9
9
R
11
Ans
.
B
T
10. ̅̅̅̅
𝐴𝐾 is a median of a triangle. The length of ̅̅̅̅
𝐴𝐾 is 15. What is the distance from vertex A to the centroid?
A) 5
B) 10
C) 15
D) 20
E) 30
A
The medians of a triangle intersect at a single
point, meaning they are concurrent. The point
of intersection is called the centroid. The
centroid divides the medians into a ratio of 2:1
where the longer segment is closer to the vertex.
x + 2x = 15  3x = 15,  x = 5  2x = 10
2x
x
Ans
.
B
K
11) Given: ̅̅̅̅
𝐴𝐷 ≅ ̅̅̅̅
𝐵𝐸 , ̅̅̅̅
𝐶𝐷 ≅ ̅̅̅̅
𝐶𝐸
̅̅̅̅
Prove: ̅̅̅̅
𝐴𝐸 ≅ 𝐵𝐷
Plan:
𝑃𝑟𝑜𝑣𝑒: 𝛥𝐶𝐴𝐸 ≅ 𝛥𝐶𝐵𝐷
C
D
E
A
B
Statements
1) ̅̅̅̅
𝐶𝐷 ≅ ̅̅̅̅
𝐶𝐸 (𝑠. ≅ 𝑠. )
2) < 𝐶 ≅< 𝐶 (𝑎. ≅ 𝑎. )
3) ̅̅̅̅
𝐴𝐷 ≅ ̅̅̅̅
𝐵𝐸
̅̅̅̅ + 𝐶𝐷
̅̅̅̅ ≅ ̅̅̅̅
̅̅̅̅
4) 𝐴𝐷
𝐵𝐸 + 𝐶𝐸
or
̅̅̅̅
𝐴𝐶 ≅ ̅̅̅̅
𝐵𝐶 (𝑠. ≅ 𝑠. )
5) ∆𝐴𝐶𝐸 ≅ ∆𝐵𝐶𝐷
̅̅̅̅ ≅ 𝐵𝐷
̅̅̅̅
5)𝐴𝐸
Reasons
1) Given
2) Reflexive Property of congruence
3) Given
4)Addition Postulate (1,3)
5) (𝑠. 𝑎. 𝑠 ≅ 𝑠. 𝑎. 𝑠. )
5) Corresponding parts of congruent
triangles are congruent
12) Construct the line containing A and perpendicular to the line containing ̅̅̅̅
𝐵𝐶 .
̅̅̅̅ . Put the compass point on A and draw
Extend 𝐵𝐶
A and
̅̅̅̅ in two locations. Mark these
arc that intersects 𝐵𝐶
intersection points. Put the compass point on one of
the intersections and draw an arc below. Using the
same opening, put the compass point on the other
intersection and draw another arc below intersecting
the first arc below. Draw a line through A and the
intersection of the two lower arcs.