Question

The four-sided geometric figure pictured is called a parallelogram. One feature of parallelograms is that opposite sides have equal lengths. The dotted line splits the parallelogram into two triangles. What is true about the congruency of the two triangles? 1)More information is needed. 2)The triangles can be proven congruent using SSS. 3)The triangles can be proven congruent using HL. 4)The triangles are not congruent.

Answer 1

B is correct answer.

Answer 2

The answer is the option
`2`

The triangles can be proven congruent using SSS

Explanation:

we know that

The property of a parallelogram are the following

a) Opposite angles are congruent

`m<A=m<C, m<B=m<D`

b) Consecutive angles are supplementary

`m<A+m<B=m<B+m<C=m<C+m<D=m<D+m<A=180\°`

c) The diagonals of a parallelogram bisect each other

d) Opposite sides are parallel and congruent

`AD=BC, AB=DC`

see the attached figure to better understand the problem

Remember that

If two triangles are congruent by SSS

then

their corresponding sides are congruent

In this problem

the triangles ABD and CDB are similar by SSS

because

`AD=BC, AB=DC` -----> Opposite sides are congruent