T ind te measure of each anglesides AB. BC and CA show that MQ17. In �

1.	T ind te measure of each anglesides AB. BC and CA show that MQ17. In ÎÎ B C DF are respectively the mid points of sides AB, BC and CA. show that AABC isdivided into four congruent triangle by joining D, E and F
Answer» As D and E are mid-points of sides AB and BC of the triangle ABC, by Theorem 1, DE \|\| AC Similarly, DF \|\| BC and EF \|\| AB Therefore ADEF, BDFE and DFCE are all parallelograms. Now DE is a diagonal of the parallelogram, therefore, ∆ BDE ≅ ∆ FED Similarly ∆ DAF ≅ ∆ FED and ∆ EFC ≅ ∆ FED So, all the four triangles are congruent. a number line is a s h o w n BEL o w a number line is s h o w n b e l o w

T ind te measure of each anglesides AB. BC and CA show that MQ17. In ÎÎ B C DF are respectively the mid points of sides AB, BC and CA. show that AABC isdivided into four congruent triangle by joining D, E and F

Answer»

As D and E are mid-points of sides AB and BC of the triangle ABC, by Theorem 1,

DE || AC

Similarly, DF || BC and EF || AB

Therefore ADEF, BDFE and DFCE are all parallelograms.

Now DE is a diagonal of the parallelogram,

therefore, ∆ BDE ≅ ∆ FED

Similarly ∆ DAF ≅ ∆ FED

and ∆ EFC ≅ ∆ FED

So, all the four triangles are congruent.

a number line is a s h o w n BEL o w

a number line is s h o w n b e l o w