True statements: B, C, E, F
Step-by-step explanation:
Right angle is at ∠BAD
∠BAD = 90 degree
Opposite angles of a parallelogram are equal
∠BAD = ∠BCD
∠ABC = ∠ADC
a) The diagonals bisect each other
Since angle on a straight line is 180 degrees
By bisecting each other, the angles are divided ito two equal parts.
∠BOC = 180/2 = 90 degree
Hence, ∠BOC is not 45 degrees
b) Since ∠BAD = 90 degree
And the diagonal bisects the vertex, the angles are divided into two equal parts
∠BAC = 90/2 = 45
∠BAC = 45 degrees
c) ∠B is the same for both
∠ABO is congruent to ∠DBA
d) From the explanation above, ∠ABC = ∠ADC = 90 degrees
Since ∠B is 90 degrees, the triangle is right angled not scalene
e) AB corresponds to DC
BD corresponds to CA
AD corresponds to AD (reflexive property)
Since the three sides of triangle ABD corresponds to the three sides of triangle DCA
Hence, triangle ABD is congruent to triangle DCA
f) ∠O = 90 degree
∠A = 45 degree
∠ D = 45 degree
In triangle AOD, two angles are equal (90 degree). Hence, triangle AOD is an isosceles triangle