Answer:
A = true
B = false
C = true
D = true
Step-by-step explanation:
Given ABCD is rectangle
1. In Rectangle opposite sides are equal.
AB is opposite to DC
thus, AB = CD
2.In rectangle adjacent sides are not equal
AD is adjacent to DC hence
AD != DC
Diagonals bisects the corner angle angle into two equal part
each angle of rectangle is 90.
Thus,
in Triangle ABE
AC bisects angle EAB
angle EAB = 90/2 = 45
DB bisects angle EBA
angle EBA = 90/2 = 45\
Length of diagonals are equal in rectangle
Also diagonals bisects each other equally
As AC and DB are diagonal
Thus, AC = DB (4)
They bisect each other at E
Thus
AE = EC(As diagonals bisects each other equally
DE = EB (diagonals bisects each other equally)
Then AE = EB
As condition for isosceles traingle is two of angles should be equal and two sides should be equal
Then , triangle ABE is isosceles based on above discussion.
Thus, Answer is
A = true
B = false
C = true
D = true
