Question

ulianna has been given two segments and the measure of an angle between them. She is trying to construct a congruent triangle. She is in the middle of one of the steps of the construction. What step is she in the process of doing?

Answer 1

Constructing the given angle using the line segment drawn

Explanation:

Given: Two line segment and one angle in between SAS congruence.

SAS congruence is visible when two triangles are similar such that they have same two sides and one angle.

Now to Draw a SAS( side,angle,side) congruent triangle three steps are followed:

1. Draw one of the measured line segment using a scale and pencil.

2. Using protractor, keep the middle of protractor on one point of line segment and draw the angle given.

3. Using a compass and scale measure the other line segment and draw an arc and finally join.

For example:

Let assume the given requirements as follows:

AB=3 cm, ∠B=45° and BC=5 cm.

Step 1: draw a line AB= 3cm using a ruler and a pencil

Step 2: Keep the protractor on B and measure angle 45°. Make a point where the angle lies and extend a line from B to this point.

Step 3: Measure 5 cm using compass and scale. Keep the point of compass on B and make an arc on extended line from B. The point where the arc meets the line from B forms point C and is joined to A.

The resultant is triangle ABC with given requirements.