Question

In the given figure ABC is an equilateral triangle.if CDE=60, show that CDE is also and equilateral.

(sorry for the blurry photo, the print came like that)

Answer 1

To show that CDE is an equilateral triangle, we need to show that all three sides of CDE have equal length, and that all three angles of CDE are equal to 60 degrees.

Since ABC is an equilateral triangle, all three sides have equal length, and all three angles have equal measure (60 degrees). This means that angles ADC, BDE, and CDA are all equal to 60 degrees.

Since angles ADC and CDA add up to 180 degrees (a straight line), the measure of angle BDE must also be equal to 60 degrees. Thus, all three angles of CDE are equal to 60 degrees.

To show that all three sides of CDE have equal length, we can use the fact that opposite sides of a parallelogram have equal length. Since CD and DE are opposite sides of parallelogram CDE, they have equal length. Similarly, CE and CD have equal length. Therefore, all three sides of CDE have equal length, and CDE is an equilateral triangle.