Question

Please solve these questions for me. i am having a difficult time understanding.

Answer 1

Answer:

1) AD=BC(corresponding parts of congruent triangles)

2)The value of x and y are 65 ° and 77.5° respectively

Step-by-step explanation:

1)

Given : AD||BC

AC bisects BD

So, AE=EC and BE=ED

We need to prove AD = BC

In ΔAED and ΔBEC

AE=EC (Given)

$\angle AED = \angel BEC$ ( Vertically opposite angles)

BE=ED (Given)

So, ΔAED ≅ ΔBEC (By SAS)

So, AD=BC(corresponding parts of congruent triangles)

Hence Proved

2)

Refer the attached figure

$\angle ABC = 90^{\circ}$

In ΔDBC

BC=DC (Given)

So,$\angle CDB=\angle DBC$(Opposite angles of equal sides are equal)

So,$\angle CDB=\angle DBC=x$

So,$\angle CDB+\angle DBC+\angle BCD = 180^{\circ}$ (Angle sum property)

x+x+50=180

2x+50=180

2x=130

x=65

So,$\angle CDB=\angle DBC=x = 65^{\circ}$

Now,

$\angle ABC = 90^{\circ}\\\angle ABC=\angle ABD+\angle DBC=\angle ABD+x=90$

So,$\angle ABD=90-x=90-65=25^{\circ}$

In ΔABD

AB = BD (Given)

So,$\angle BAD=\angle BDA$(Opposite angles of equal sides are equal)

So,$\angle BAD=\angle BDA=y$

So,$\angle BAD+\angle BDA+\angle ABD = 180^{\circ}$(Angle Sum property)

y+y+25=180

2y=180-25

2y=155

y=77.5

So, The value of x and y are 65 ° and 77.5° respectively