Question

geometry
© 2019 kuta software llc. all rights reserved.
3.4 constructing triangles
construct a triangle given the three side lengths.
1)
side 1:
side 2:
side 3:
2)
side 1:
side 2:
side 3:
3)
side 1:
side 2:
side 3:
construct triangle abc given two sides and the included angle.
4)
a
a
c
a
b
5)
a
a
c
a
b

Explanation:

Step1: Recall triangle - construction rules

For constructing a triangle given three side - lengths, we first check the triangle inequality theorem: the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. For constructing a triangle given two sides and the included angle, we use a compass and a straight - edge.

Step2: Construction steps for three - side lengths

1. Draw one side (say Side 1) using a straight - edge.
2. With one end of Side 1 as the center, use a compass to draw an arc with a radius equal to the length of Side 2.
3. With the other end of Side 1 as the center, use a compass to draw an arc with a radius equal to the length of Side 3. The intersection of these two arcs gives the third vertex of the triangle.

Step3: Construction steps for two sides and included angle

1. Draw one of the given sides (say side AB) using a straight - edge.
2. Using a protractor, construct the given included angle at one of the endpoints of side AB (say at point A).
3. With point A as the center, use a compass to draw an arc with a radius equal to the length of the other given side. The intersection of the ray of the constructed angle and the arc gives the third vertex of the triangle (point C).

Since no specific side - length or angle - measure values are given in the problem, we can't provide a numerical answer. But the general construction steps are as above.

Answer:

The construction steps for constructing a triangle given three side - lengths and two sides and the included angle are provided above.