Use geometry software to draw a triangle whose sides have the following lengths: 2 units, 3 units, and 4 units.

**Step 1 :**

Draw the segments.

**Step 2 :**

Let AB be the base of the triangle. Place point C on top of point B and point E on top of point A.

**Step 3 :**

Using the points C and E as fixed vertices, rotate points F and D to see if they will meet in a single point.

Note that the line segments form a triangle.

Repeat step 1 and step 2, but use a different segment as the base. Do the segments form a triangle? If so, is it the same as the original triangle ?

**Answer : **

Yes; the triangle has the same size and shape as the original.

**Question 2 : **

Use geometry software to draw a triangle with sides of length 2, 3, and 6 units, and one with sides of length 2, 3, and 5 units. Do the line segments form triangles? How does the sum of the lengths of the two shorter sides of each triangle compare to the length of the third side ?

**Answer : **

1 st : no, 2 + 3 < 6

2 nd : no; 2 + 3 = 5

**Question 3 : **

Do two segments of lengths a and b units and a longer segment of length c units form one triangle, more than one, or none ?

**Answer : **

One triangle if a + b > c ; none if a + b ≤ c.

Use a ruler and a protractor to draw a triangle for the given measures.

Angles : 30° and 80°

Length of included side : 2 inches

**Step 1 :**

Use a ruler to draw a line that is 2 inches long. This will be the included side.

**Step 2 :**

Place the center of the protractor on the left end of the 2-in. line. Then make a 30°-angle mark.

**Step 3 :**

Draw a line connecting the left side of the 2-in. line and the 30°-angle mark. This will be the 30° angle.

**Step 4 :**

Repeat Step 2 on the right side of the triangle to construct the 80° angle.

**Step 5 :**

The side of the 80° angle and the side of the 30° angle will intersect. This is Triangle 1 with angles of 30° and 80° and an included side of 2 inches.

**Question : **

Will a triangle be unique if you know all three angle measures but no side lengths ?

**Answer : **

Yes, the two angles and the length of the included side determine the point at which the sides meet. The triangle is unique.

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