Question 3 - Figure it out - Page 8, 9 - Chapter 1 Class 7 - Geometric Twins (Ganita Prakash II)

Transcript

Question 3 In the figure below, AB = AD, CB = CD. Can you identify any pair of congruent triangles? If yes, explain why they are congruent. Does AC divide ∠BAD and ∠BCD into two equal parts? Give reasons.We can see that in ∆ ABC & ∆ ADC AB = AD CB = CD Side AC is common, AC = AC Thus, all 3 sides are equal in both triangles. So, triangles are congruent by SSS (Side-Side-Side) Congruence Rule Finding which points match Since ∆ ADC when flipped superimposes ∆ ABC Points which match are A ⟷ A B ⟷ D C ⟷ C So, we can write By SSS Congruence rule ∆ ABC ≅ ∆ ADC Now, our next question is Does AC divide ∠BAD and ∠BCD into two equal parts? Give reasons. Since ∆ ABC ≅ ∆ ADC By Corresponding Parts of Congruent Triangles (CPCT) ∠ BAC = ∠ DAC So, we can say AC cuts ∠ BAD in half Similarly by CPCT ∠ BCA = ∠ DCA So, we can say AC cuts ∠ BCD in half Hence, AC divides ∠BAD and ∠BCD into two equal parts