# ABCD is a rhombus

Given,

ABCD is a rhombus.DE is the altitude on AB then AE = EB.

In a ΔAED and ΔBED,
DE = DE (common line)
AED = BED (right angle)
AE = EB (DE is an altitude)
ΔAED ΔBED (SAS property)

But AD = AB (sides of rhombus are equal)
ABD is an equilateral triangle.
A = 60
A = C = 60 (opposite angles of rhombus are equal)
But Sum of adjacent angles of a rhombus is supplementary.
ABC + BCD = 180
ABC + 60 = 180
ABC = 180-60 = 120
ABC = ADC = 120 (opposite angles of rhombus are equal)
Angles of rhombus are A = 60, C = 60, B = 120, D = 120

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses
RELATED QUESTIONS :

The lengthsRS Aggarwal & V Aggarwal - Mathematics

In each of RS Aggarwal & V Aggarwal - Mathematics

If the bisectors RD Sharma - Mathematics

In Fig. 14.113, PRD Sharma - Mathematics

In Fig. 14.114, ARD Sharma - Mathematics

Each side oRS Aggarwal & V Aggarwal - Mathematics

If ABCD is a rhomRD Sharma - Mathematics

If ABCD is a rectRD Sharma - Mathematics