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Step-5

Title:

Grade: 10-a Lesson: S2-L2

Explanation:

Description: 5

From the figure we can observe that
$d5$

QN is perpendicualr to RP and MO and
MP is bisects of QN at S

Consider \$\triangle PQS\$ and \$\triangle MNS\$.

\begin{align} PQ &= MN \\ \angle PQS &= \angle MNS \tag{Given} \\ \angle PSQ &= \angle MSN \tag{Alternate interior angles} \\ \end{align}

So, \begin{align} \triangle PQS \cong \triangle MNS \\ \end{align}

Henced proved that \$\triangle PQS\$ \$\cong\$ \$\triangle MNS\$ by the ASA congruence rule.

$d5$

Steps	Statment	Solution
1	Given	From the figure we can observe that
2	Given side of triangles	QN is perpendicualr to RP and MO and MP is bisects of QN at S .
3	Consider angles	\$\triangle PQS\$ and \$\triangle MNS\$
4	Side	PQ = MN
5	Alternate interior angles	\$angle PQS = angle MNS\$ and \$angle PSQ = angle MSN\$
6	Congruency	\$\triangle PQS \cong \triangle MNS\$
7	Prove that	Henced proved that \$\triangle PQS\$ \$\cong\$ \$\triangle MNS\$ by the ASA congruence rule.

Steps

Statment

Solution

Given

From the figure we can observe that

Given side of triangles

QN is perpendicualr to RP and MO and MP is bisects of QN at S .

Consider angles

\$\triangle PQS\$ and \$\triangle MNS\$

Side

PQ = MN

Alternate interior angles

\$angle PQS = angle MNS\$ and \$angle PSQ = angle MSN\$

Congruency

\$\triangle PQS \cong \triangle MNS\$

Prove that

Henced proved that \$\triangle PQS\$ \$\cong\$ \$\triangle MNS\$ by the ASA congruence rule.