Question 4 - Figure it out - Page 60 - Chapter 3 Class 8 - Proportional Reasoning-2 (Ganita Prakash II)

Transcript

Question 4 Construct a triangle with sidelengths in the ratio 3 : 4 : 5. Will all the triangles drawn with this ratio of sidelengths be congruent to each other? Why or why not? Since the sides are in the ratio 3 : 4 : 5, we can make triangle with sides 3, 4, 5 Multiplying ratio by 2 – 6, 8, 10 Or multiplying ratio by any number, say 10 – 30, 40, 50 By Triangle inequality Sum of two sides > Third side Here, 3 + 4 > 5 Thus, triangle is possible Let’s draw Triangle with sides 3 cm, 4 cm and 5 cm First we draw a rough sketch Let’s try to construct it now Steps of construction 1. Draw a line segment AB of length 4 cm 2. Since AC = 3 cm. Taking 3 cm as radius, and A as center, we draw a full circle lightly 3. Since BC = 5 cm. Taking 5 cm as radius, and B as center, we draw a full circle lightly Now, where these two circles intersect is our point C 5. Join AC and BC and label the sides Thus, Δ ABC is the required triangle Now, the next part of our question is Will all the triangles drawn with ratio 3 : 4 : 5 of sidelengths be congruent to each other? Why or why not? Congruent means same shape and size But, here triangles have same shape and not same size Thus, these triangles are not congruent (they are similar)