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Potpourri
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Angles
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100
The point of concurrency for the altitudes of a triangle is called the
orthocenter
100
1. Construct an equilateral triangle using a compass and a straightedge, given AB as one side.
Measure side AB with compass. Make arc from Point A above the line. Move compass to Point B and make another arc. Mark where the arcs meet and connect the points.
100
5. Find the value of x and y.
x = 103 y= 77
100
11. Find the value of x and y in the diagram below. Give reasons for your calculations.
x = 50 y = 140 Straight line has 180 degrees
100
The point of concurrency for the medians is called the
centroid
200
Angles that add up to 90 degrees.
Complementary
200
2. Copy then bisect the following angle using a compass and a straightedge.
Draw new point and line. Make compass go through first angle and mark the points. Move compass to new line and do the same thing. Measure two new points and go from the point where arc goes through new line to create angle and then bisect it.
200
6. Name a pair of supplementary angles, a pair of adjacent angles and a pair of vertical angles.
Supplementary Adjacent Vertical -4 and 5 -1 and 2 -3 and 5 -3 and 4 -3 and 4 -4 and 6 -3 and 6 -3 and 6 -1 and 2 -4 and 5 -5 and 6 -5 and 6
200
10. In the diagram below, l is parallel to m. If angle 1 is 63, find angle 2.
27
200
14a. Find measure of angle a, angle e and angle k.
angle a = 43. alternate interior angles angle e = 43 angles in a triangle = 180 angle k = 94 angles that form a straight line = 180
300
Describe the relationship between the interior angles of a triangle and the exterior angle.
The exterior angle of a triangle is equal to the sum of the two interior angles of a triangle.
300
3a. Construct the perpendicular bisector of the given segment.
Measure line. Make arc above and below the line from first point. Move compass to second point and make two arcs again.
300
7. Suppose the measure of angle ABC = 110, what is the measure of angle DBC?
40 degrees
300
12. Find the unknown angles. Give reasons for your solutions.
angle a = 48- alternate interior angles ange b = 62- same side interior angles are supplementary
300
14d. Find measure of angle b.
b= 20 an isosceles triangle has two congruent sides and angles angles in a triangle = 180
400
What is a perpendicular bisector?
A line that divides another line into two congruent parts at a right angle (90 degrees)
400
3b. Construct a line perpendicular to ST through the line at point P.
Put compass on point P and make it go through line ST twice. Use those points for perpendicular bisector.
400
9. Lines p and q are intersected by line r, as show below. Find the value of x that would make p parallel to q.
17
400
14c. Find the measure of angle A.
70. Angles in a straight line = 180 Isosceles triangles have two congruent sides and angles.
400
14b. Find the measure of angle x.
x = 128 alternate interior angles the exterior angle of a triangle equals the sum of the two interior angles
500
16. Given the following diagram, fill in the proof.
1. Angles that form a straight line add to 180. 2. Angles that form a straight line add to 180. 3. Angles in a triangle add to 180. 4. Substitution Property 5. Subtraction Property
500
4. The diagram below shows the construction of the perpendicular bisector of AB. Determine if each of the following are true or false.
-True -True -True -True
500
8. Find the values of x and y.
x= 30 y= 65 -Straight line has 180 degrees
500
13. In the diagram below, FE bisects AC at B and GE bisects BD at C. Which statement is always true.
1.
500
15. Prove the sum of the labeled angles is 180.
1. Reflexive property 2. Angles that form a straight line = 180