Download Mu Alpha Theta January Regional Geometry Team

Mu Alpha Theta January Regional
Geometry
Team Questions
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1.
In the ABC, A + B = 130 and A + C = 110 . How large is A?
2.
The sum of the two exterior angles formed by extending the hypotenuse of a right
triangle is how many degrees?
3.
Find the number of degrees in the angle formed by two diagonals drawn from the same
vertex of a regular pentagon.
4.
In a square of base 5, a 3-4-5 right triangle is positioned as shown below. Determine the
distance x:
E
A
B
F
4
D
5.
3
C
5
o
In the triangle ABC, AC=BC and AD bisects angle A. If ADC=114 , then what is the
measure of C?
6. The bases of an isosceles trapezoid are AB=15 inches and DC=9 inches respectively;
each leg is 5 inches. Find the length of a diagonal.
D
A
C
B
7.
The perimeter of a rhombus is 80 cm, and one diagonal is 14 cm long. Find the length of
the other diagonal.
8.
If the sum of the interior angles of a polygon equals four times the sum of the exterior
angles, how many sides does the polygon have?
9.
If the segments of the hypotenuse of a right triangle made by the altitude to the
hypotenuse are 3 and 12, find the altitude.
Mu Alpha Theta January Regional
Geometry
Team Questions
10. Suppose the medians AA' and BB' of triangle ABC intersect at right angles. If BC = 3
and AC = 4, what is the length of side AB?
11.
The sides of a right triangle are a, a+d, and a+2d, with a and d both positive. Find the
ratio of a to d.
12.
HIJK and DCBA are congruent parallelograms, with altitude HL. HK=10 cm, LJ = 8 cm,
2
and the area of ABCD is 112cm . What is the length of altitude DM?
I
H
C
D
10
M
K
A
L
B
J
8
13
The coordinates of the vertices of ABC are A(-5,1), B(-2,3) and C(-4,7). The triangle is
reflected over the line x=2. What is the sum of the x-coordinates of the images of points
A, B, and C?
14.
An isosceles triangle has lengths 6x+40, 4x+104, and 7x-23. What is the greatest
possible perimeter?
15.
Two congruent regular polygons are placed side-by-side so they share a common side.
The angle formed between the polygons is a right angle. How many sides does each
polygon have?