Chapter 14.6, Problem 1PSA

To determine

To construct the triangle by using the given criterion.

Explanation of Solution

Given:

The given criterion is ASA.

Calculation:

The triangle by ASA criterion can be constructed as follows-

Step 1- We are given the triangle as follows-

  

Step 2- Determine the measure of the third angle as follows-

  $\angle C=180-(\angle A+\angle B)$

Step 3- First draw the line BC and draw the angle B and angle C.

  

Step 4- Join all the points to get the triangle ABC as follows-

  

To determine

To construct the triangle by using the given criterion.

Explanation of Solution

Given:

The given criterion is SSS.

Calculation:

The triangle by SSS criterion can be constructed as follows-

Step 1- We are given the triangle as follows-

Step 2- Draw all the base line segment BC of given length.

Step 3- Now, at point B mark an arc of given length of second side.

Sep 4- similarly at point C mark an arc of given length of third side.

Step 4- Join all the points to get the triangle ABC as follows-

  

To determine

To construct the triangle by using the given criterion.

Explanation of Solution

Given:

The given criterion is HL.

Calculation:

The triangle by HL criterion can be constructed as follows-

The right triangle given the hypotenuse and the altitude of the hypotenuse can be constructed as follows-

Step 1- Draw the circle as the diameter equal to the hypotenuse of the given triangle.

Step 2- Drop the perpendicular to the hypotenuse from any point on the circle whose length equals to the altitude.

Step 3- Now, join all the three points.

Step 5- Join all the vertices to get the required right triangle.