Construct triangles for the following measurements: 75°, 5 cm, 75°. Class 7

Construct triangles for the following measurements: 75°, 5 cm, 75°. Class 7

Question 1.

Construct triangles for the following measurements: Class 7

(a) 75°, 5 cm, 75°

(b) 25°, 3 cm, 60°

(c) 120°, 6 cm, 30°

Solution:

Do as directed. Following the same steps 1, 2 and 3 as given for 45°, 5 cm, 80°.

Construct a triangle ABC where AB = 5 cm, ∠A = 45° and ∠B = 80°.

Let us take the given side as the base.

Step 1: Draw the base AB of length 5 cm.

Step 2: Draw ∠A and ∠B of measures 45°, and 80° respectively.

Step 3: The point of intersection of the two new line segments is the third vertex C.

Question 2.

Do triangles exist for every combination of two angles and their included side? Explore. Class 7

Solution:

No. If sum of given two angles is greater or equal to 180°, the construction of triangles is not possible.

Question 3.

Find examples of measurements of two angles with the included side where a triangle is not possible. Class 7

Solution:

120°, 3 cm, 60°, 80°, 5 cm, 110°