FAQs on Construction of Triangle: Given Lengths of 2 Sides and Measure of Angle between Them(SAS Criterion)

Question 1

1. How do you construct a triangle when given the lengths of two sides and the measure of the angle between them?

Accepted Answer

Ans. To construct a triangle using the SAS criterion, start by drawing a line segment to represent one of the given sides. Then, using a protractor, measure and mark the angle between the two sides. From the endpoint of the first side, use a compass to measure the length of the second side and draw an arc. Finally, connect the endpoint of the first side to the point where the arc intersects the line segment, completing the triangle.

Question 2

2. Can you construct a triangle with any combination of side lengths and angle measures using the SAS criterion?

Accepted Answer

Ans. No, not all combinations of side lengths and angle measures will result in a valid triangle. In order for a triangle to exist, the sum of any two sides must be greater than the third side. Additionally, the angle measure between the two given sides must be less than 180 degrees.

Question 3

3. What is the importance of the SAS criterion in triangle construction?

Accepted Answer

Ans. The SAS criterion is important in triangle construction because it allows us to construct triangles using specific measurements. By knowing the lengths of two sides and the measure of the angle between them, we can accurately create triangles with precise dimensions.

Question 4

4. Can you use the SAS criterion to construct a unique triangle?

Accepted Answer

Ans. No, the SAS criterion does not guarantee a unique triangle. It is possible to have multiple triangles with the same side lengths and angle measure. However, these triangles may be congruent to each other, meaning they have the same shape and size.

Question 5

5. What are some other criteria for triangle construction?

Accepted Answer

Ans. In addition to the SAS criterion, there are two other commonly used criteria for triangle construction. These are the SSS criterion (given the lengths of three sides) and the ASA criterion (given the measure of two angles and the length of the side between them). These criteria provide different combinations of measurements for constructing triangles.

Construction of Triangle Given Lengths of 2 Sides and Measure of Angle

Mathematics for Grade 7

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