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Step-4

Title:

Grade: 10-a Lesson: S2-L1

Explanation:

$4$

Give that ABCD is a parallelogram, BD is the diagonal of the parallelogram.

Consider \$\triangle CDB\$ and \$triangle ADB\$.

\begin{align} BC = DA \tag{Given} \\ BC // DA \tag{Given} \\ DB = DB \tag{common side} \\ \end{align}

$4.1$

ABCD is a parallelogram.
In a parallelogram the opposite interior angles are equal.

Therefore \begin{align} \angle BCD = \angle BAD \\ \end{align}

Henced proved that \$\triangleCDB\$ and \$\cong\$ \$\triangleADB\$ by the SAS congruence rule.

$4.1$

Steps	Statment	Solution
1	Given	Give that ABCD is a parallelogram, BD is the diagonal of the parallelogram.
2	Consider trianles	\$\triangle CDB\$ and \$triangle ADB\$
3	Side of triangles	BC = DA and BC // DA and DB = DB [common side]
4		ABCD is a parallelogram. In a parallelogram the opposite interior angles are equal.
5	Angles	\$\angleBCD and \angleBAD\$
6	Congruency	\$\triangleCDB \cong \triangleADB\$
7	Prove that	Henced prove that \$\triangleNQM\$ and \$\cong\$ \$\trianglePQO\$ by the SAS congruence rule.

Steps

Statment

Solution

Given

Give that ABCD is a parallelogram, BD is the diagonal of the parallelogram.

Consider trianles

\$\triangle CDB\$ and \$triangle ADB\$

Side of triangles

BC = DA and BC // DA and DB = DB [common side]

ABCD is a parallelogram. In a parallelogram the opposite interior angles are equal.

Angles

\$\angleBCD and \angleBAD\$

Congruency

\$\triangleCDB \cong \triangleADB\$

Prove that

Henced prove that \$\triangleNQM\$ and \$\cong\$ \$\trianglePQO\$ by the SAS congruence rule.