Triangles - Sides
Do line segments of length 4, 5, and 8 form a triangle? Explain.
Yes. The sum of the smallest sides is greater than the longest side. ( 4+5= 9; 9 is greater than 8)
Two angles of a triangle are 45 and 90. What is the third angle?
45 degrees
What is the angle measure that is complementary to 46 degrees?
44 degrees
46 + 44 = 90
Sides of length 3, 5, and 10
Creates:
One triangle, many different triangles, or no triangles?
no triangles
True or False. For two angles to be complements they must be adjacent.
False. The only requirement is that the two angles must add to 90 degrees.
Can the following sides form a triangle? Explain.
6.5, 4.333, 2.025
No. Since the sum of the two shortest sides is 6.358 and it is less than the length of the longer side (6.5) no triangle can be made.
In a right triangle one of the angles measures 38 degrees. What is the measure of the missing angle?
52 degrees
What angle is a supplement to 35 degrees?
145 degrees
35 + 135 = 180 degrees
Angles of 60 degrees, 60 degrees, and 60 degrees
Creates:
One triangle, many different triangles, or no triangles?
many different triangles
Describe an impossible triangle to satisfy your opponent!
Answer. The student should have mentioned angles that do not add up to 180 degrees OR three side lengths where the sum of the two shorter sides is not greater than the 3rd side.
True or False. As long as the length of the two shortest sides combined is greater than or equal to the longest side, a triangle can be formed.
False. The two shortest sides combined have to be greater than the 3rd side.
Three angles of a triangle are 70 degrees, x-4, and x. What is the value of x?
x = 57
70 + x-4 + x = 180
2x + 66 = 180
- 66 -66
2x = 114 x = 57
True or False. It is impossible for an obtuse angle to have a complementary angle. Explain.
True. Since an obtuse angle is already greater than 90 degrees, it cannot have a complement.
Angles of 95 degrees, 25 degrees, and 70 degrees
Creates:
One triangle, many different triangles, or no triangles?
no triangles
The sum of the angles is 190 degrees, so no triangle can be formed.
This question is about a triangle: If angle A is 40.7 degrees and angle B is 15.6 degrees, what is the measurement of angle C?
123.7 degrees
40.7 + 15.6 = 56.3 180 - 56.3 = 123.7 degrees
If two sides of a triangle are 3 and 5, describe the values that are possible for the 3rd side.
The third side must be greater than 2, but less than 8.
In an isosceles triangle one angle measures 102 degrees. Explain how to determine the measure of the other two angles. What are their degree measures?
39 degrees each.
Two angles are congruent in isosceles triangles. Since 102 degrees is an obtuse angle we know it cannot be one of the congruent angles (Their sum would be greater than 180 degrees). 78 degrees are left for the other two angles, making each 39.
Suppose that angle A and angle B are complements. If the measure of angle A is 2x+5 and the measure of angle B is x-35, what are their degree measurements?
85 degrees and 5 degrees.
2x+5 + x - 35 = 90
3x - 30 = 90
+30 +30
3x = 120 x = 40 2(40) + 5 = 85 40 -35 = 5
A right triangle that has a base of 9 cm and a height of 5 cm.
Creates:
One triangle, many different triangles, or no triangles?
One triangle.
Boards come in 4 lengths at the lumber store. (6ft, 8ft, 12ft, and 18ft). A dad wants to buy 3 boards to build a triangular play area for his kids without cutting. He already selected a 18ft board. Explain what other two boards he could select.
There are several answers. One combination that he can't select is an 6ft and a 8ft. As long as the student student showed that the two shorter boards together are longer than 18ft, they get 400 points.
If two sides of a triangle are 13 1/2 and 15, what are the possible values for the 3rd side?
The third side must be greater than 1 1/2, but less than 28 1/2.
In a triangle, one angle measures 36 degrees. The other two angles have the relationship where one is twice the measurement of the other. What are the measurement of each angle in the triangle?
36, 48, and 96 degrees.
180 - 36 = 144 degrees
x and 2x are the missing angles
3x = 144
x = 48 2x = 96
Suppose that angle A and angle B are supplements. If the measure of angle A is 2x+5 and the measure of angle B is x-35, what are their degree measurements?
145 degrees and 35 degrees
2x + 5 + x - 35 = 180
3x - 30 = 180
+30 +30
3x = 210 x = 70 2(70) + 5 = 145 70 -35 = 35
An isosceles triangle of lengths 5, 5, and 10
Creates:
One triangle, many different triangles, or no triangles?
No triangles
5 +5 = 10 and the two shortest sides have to be greater than the third side.
The measure of the supplement of an angle is 8 less than three times the measure of the angle. Find the measure of the angle and its supplement.
47 and 133.
The two angles are x and 3x - 8.
4x - 8 = 180
+8 +8
4x = 188 x = 47 3 (47) - 8 = 133