### Learning Targets:

Given two side lengths and also one edge measure, I can draw various triangles with these measurements or present that these measurements recognize one distinct triangle or no triangle.

You are watching: Based on the given angle measures, which triangle has side length measures that could be correct?

Draw a 40^\\circ angle.Use a compass to make sure both sides of her angle have a length of 5 centimeters.If you attach the ends of the political parties you drew to make a triangle, is the 3rd side much longer or much shorter than 5 centimeters? How can you use a compass to define your answer?

Use the applet to draw triangles.

Draw as many different triangles together you deserve to with each of these sets of measurements:

One angle steps 40^\\circ , one side procedures 4 cm and also one side actions 5 cm.Two sides measure 6 cm and also one angle measures 100^\\circ .

Did either of this sets the measurements identify one unique triangle? just how do girlfriend know?

Use the applet to draw triangles. Sides can overlap.

Draw as plenty of different triangles as you can with every of this sets of measurements:One angle measures 50^\\circ , one measures 60^\\circ , and also one steps 70^\\circ .One angle actions 50^\\circ , one measures 60^\\circ , and one procedures 100^\\circ .Did either of this sets that measurements identify one distinctive triangle? exactly how do you know?

### Are you ready for more?

Using just the point, segment, and also compass tools provided, develop an it is intended triangle. Girlfriend are only successful if the triangle remains equilateral while dragging the vertices around.

## Lesson 10 Summary

A triangle has six measures: 3 side lengths and three angle measures.

If we are given three measures, climate sometimes, over there is no triangle that have the right to be made. For example, there is no triangle through side lengths 1, 2, 5, and also there is no triangle through all three angles measuring 150^\\circ . Sometimes, only one triangle can be made. By this we average that any kind of triangle we make will certainly be the same, having the very same six measures. For example, if a triangle can be made v three offered side lengths, climate the corresponding angles will have actually the same measures. One more example is displayed here: an edge measuring 45^\\circ in between two next lengths the 6 and also 8 units. With this information, one distinctive triangle deserve to be made. Sometimes, two or more different triangles have the right to be made through three given measures. Because that example, right here are two different triangles that can be made with an edge measuring 45^\\circ and also side lengths 6 and 8. An alert the edge is not between the provided sides.

Three pieces of information about a triangle’s next lengths and also angle steps may recognize no triangles, one distinctive triangle, or an ext than one triangle. It depends on the information.

## Lesson 10 practice Problems

A triangle has sides of size 7 cm, 4 cm, and also 5 cm. How countless unique triangles can be drawn that fit that description? define or present your reasoning.

A triangle has actually one side that is 5 units long and also an surrounding angle that procedures 25^\\circ . The two various other angles in the triangle measure 90^\\circ and also 65^\\circ . Finish the two diagrams to develop two different triangles through these measurements. Is it possible to make a triangle that has angles measure 90 degrees, 30 degrees, and also 100 degrees? If so, draw an example. If not, explain your reasoning.

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Segments CD , abdominal , and FG crossing at suggest E . Angle FEC is a best angle. Identify any type of pairs of angles that are complementary.