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January Regional
Geometry Team Question #1
How many of the following statements are true?
A. The sum of the exterior angles of any shape is 360 degrees.
B. Given that the following statement is true: “If it rains, then Travis will not go to the
beach.” Is the statement “Travis will go to the beach if it does not rain.” true?
C. The slopes of perpendicular lines are equal.
D. Vertical angles are congruent.
January Regional
Geometry Team Question #1
How many of the following statements are true?
A. The sum of the exterior angles of any shape is 360 degrees.
B. Given that the following statement is true: “If it rains, then Travis will not go to the
beach.” Is the statement “Travis will go to the beach if it does not rain.” true?
C. The slopes of perpendicular lines are equal
D. Vertical angles are congruent.
January Regional
Geometry Team Question #2
Find the sum of the angles of a 5-pointed star.
January Regional
Find the sum of the angles of a 5-pointed star.
Geometry Team Question #2
January Regional
Geometry Team Question #3
A. How many diagonals does a 20-gon have?
B. How many sides does a reg. polygon in which each angle is 156 degrees have?
C. What is the perimeter of a rhombus with diagonals 12, and 14.
D. How many polygons have less than 9 diagonals?
Find the value of 2A + B – C + D
January Regional
Geometry Team Question #3
A. How many diagonals does a 20-gon have?
B. How many sides does a reg. polygon in which each angle is 156 degrees have?
C. What is the perimeter of a rhombus with diagonals 12, and 14.
D. How many polygons have less than 9 diagonals?
Find the value of 2A + B – C + D
January Regional
Geometry Team Question #4
A. What is the sum of all angles formed by two intersecting lines?
B. How many diagonals are there in a polygon with 15 sides?
C. When categorized by side length, there are only 3 kinds of triangles. (worth 1 point if
true, worth -1 if false.)
D. How many sides does polygon ABCDEFGHIJKLMNOP have?
Find the value of A + B + C + D
January Regional
Geometry Team Question #4
A. What is the sum of all angles formed by two intersecting lines?
B. How many diagonals are there in a polygon with 15 sides?
C. When categorized by side length, there are only 3 kinds of triangles. (worth 1 point if
true, worth -1 if false.)
D. How many sides does polygon ABCDEFGHIJKLMNOP have?
Find the value of A + B + C + D
January Regional
Geometry Team Question #5
Johan is putting a frame around a photograph of himself. If the frame is 2 inches wide, and
the picture has dimensions of 8 x 10 inches, find the opposite inverse reciprocal of the
perimeter of the finished product.
January Regional
Geometry Team Question #5
Johan is putting a frame around a photograph of himself. If the frame is 2 inches wide, and
the picture has dimensions of 8 x 10 inches, find the opposite inverse reciprocal of the
perimeter of the finished product.
January Regional
Geometry Team Question #6
A. Find the perimeter of a rhombus with diagonals of length 14, and 48.
B. Find the length of the diagonal of a square with perimeter 900.
C. Find the sum of the coordinates of the midpoint of the line segment with endpoints
(8, 2) and (3, -4)
D. Find the distance between (5, 7) and (-12, 3).
Find the value of
January Regional
Geometry Team Question #6
A. Find the perimeter of a rhombus with diagonals of length 14, and 48.
B. Find the length of the diagonal of a square with perimeter 900.
C. Find the sum of the coordinates of the midpoint of the line segment with endpoints
(8, 2) and (3, -4)
D. Find the distance between (5, 7) and (-12, 3).
Find the value of
January Regional
Geometry Team Question #7
In isosceles triangle ABC with angles B and C congruent; angle bisector AD is drawn from
vertex A to side BC. Find the length of the angle bisector given that side AC is 10, and side
BC is 15. Express the answer as a rationalized fraction.
January Regional
Geometry Team Question #7
In isosceles triangle ABC with angles B and C congruent; angle bisector AD is drawn from
vertex A to side BC. Find the length of the angle bisector given that side AC is 10, and side
BC is 15. Express the answer as a rationalized fraction.
January Regional
Geometry Team Question #8
Let A = The compliment of the smallest angle of a triangle with angles (x – 3), (10x + 3),
and (3x + 12).
Let B = The largest possible integral value of x for a triangle with side lengths 8, 13, and x.
Let C = The smallest possible integral value of z for a triangle with sides lengths 14, 18, and
z.
Let D = The length of the longest side a triangle with coordinates (-5, 3), (1, 2), and (3, 1).
Find the value of
January Regional
Geometry Team Question #8
Let A = The compliment of the smallest angle of a triangle with angles (x – 3), (10x + 3),
and (3x + 12).
Let B = The largest possible integral value of x for a triangle with side lengths 8, 13, and x.
Let C = The smallest possible integral value of z for a triangle with sides lengths 14, 18, and
z.
Let D = The length of the longest side a triangle with coordinates (-5, 3), (1, 2), and (3, 1).
Find the value of
January Regional
Geometry Team Question #9
A = The sum of the squares of the angles of a regular nonagon.
B = The number of points at which skew lines intersect
Find 6A – B
January Regional
Geometry Team Question #9
A = The sum of the squares of the angles of a regular nonagon.
B = The number of points at which skew lines intersect
Find 6A – B
January Regional
Geometry Team Question #10
Find the sum of the measures of the interior angles in a hendecagon.
January Regional
Geometry Team Question #10
Find the sum of the measures of the interior angles in a hendecagon.
January Regional
Geometry Team Question #11
Each of the following statements is assigned a point value. If a statement is true, it is equal to
the value next to it. If a statement is false, it has a value of -1. Find the sum of the true/false
values of each statement.
(5) The perimeter of a regular heptagon with side length 7 is 77.
(3) The contrapositive of a conditional statement is always true if the statement is true.
(1) If line A is parallel to line B, and line C is perpendicular to line A, then line C is always
perpendicular to line B.
(0) The diagonals of a rectangle bisect the angles of the rectangle.
January Regional
Geometry Team Question #11
Each of the following statements is assigned a point value. If a statement is true, it is equal to
the value next to it. If a statement is false, it has a value of -1. Find the sum of the true/false
values of each statement.
(5) The perimeter of a regular heptagon with side length 7 is 77.
(3) The contrapositive of a conditional statement is always true if the statement is true.
(1) If line A is parallel to line B, and line C is perpendicular to line A, then line C is always
perpendicular to line B.
(0) The diagonals of a rectangle bisect the angles of the rectangle.
January Regional
Geometry Team Question #12
A. In how many ways can you arrange 6 points on a circle?
B. How many planes can be formed by 12 non-collinear points?
C. How many arcs can be formed by 7 points on a circle?
D. If the ratio of the side lengths of 2 similar triangles is 2/3. What is the ratio of the sum
of their angle measures?
Find the value of A + B + C + D
January Regional
Geometry Team Question #12
A. In how many ways can you arrange 6 points on a circle?
B. How many planes can be formed by 12 non-collinear points?
C. How many arcs can be formed by 7 points on a circle?
D. If the ratio of the side lengths of 2 similar triangles is 2/3. What is the ratio of the sum
of their angle measures?
Find the value of A + B + C + D
January Regional
Geometry Team Question #13
3 cuts are made along a piece of string that is 125 cm long, producing four pieces of string.
The shortest piece of string is 1/3 the length of the longest piece. The second to longest piece
of string is 15 less than the longest piece. The remaining piece of string is 1/2 the length of
the longest piece of string. Find the length of the shortest piece of string.
January Regional
Geometry Team Question #13
3 cuts are made along a piece of string that is 125 cm long, producing four pieces of string.
The shortest piece of string is 1/3 the length of the longest piece. The second to longest piece
of string is 15 less than the longest piece. The remaining piece of string is 1/2 the length of
the longest piece of string. Find the length of the shortest piece of string.
January Regional
Geometry Team Question #14
A rope is stretched from the top of tower A to the middle of tower B. The same is done from
tower B to tower A. If tower A is 12 meters high and tower B is 8 meters high. how far from
the ground is the point at which the two ropes intersect?
January Regional
Geometry Team Question #14
A rope is stretched from the top of tower A to the middle of tower B. The same is done from
tower B to tower A. If tower A is 12 meters high and tower B is 8 meters high. how far from
the ground is the point at which the two ropes intersect?
January Regional
Geometry Team Question #15
Given triangles ACB and CDE, and that AE and BD are both line segments. By which
triangle congruency theorem are the two triangles congruent?
January Regional
Geometry Team Question #15
Given triangles ACB and CDE, and that AE and BD are both line segments. By which
triangle congruency theorem are the two triangles congruent?