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Step-3

Title:

Grade: 10-a Lesson: S2-L1

Explanation:

$3$

Give that MNOP is a square, NP and MO are the diagonals of the square meets at a point Q.

From the we can observe that

\begin{align} NQ = PQ \\ QM = QO \\ \end{align}

Also angles, \$\angle NQM\$ and \$\angle PQO\$.

Since angles, \$\angle NQM\$ and \$\angle PQO\$ form a pair of vertically opposite angles, we have

$3.1$

\begin{align} \angle NQM = \angle PQO \\ \end{align}

So, \begin{align} \triangle NQM \cong \triangle PQO \\ \end{align}

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

From the figure we can observe that

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$3.1$

Steps	Statment	Solution
1	Given	Give that MNOP is a square, NP and MO are the diagonals of the square meets at a point Q.
2	Side of triangles	NQ = PQ and QM = QO
3	Angles	\$\angleNQM and \anglePQO\$
4		Since angles, \$angleNQM and \anglePQO\$ from a pair vertically opposite angles we have
5	So	\$\angleNQM and \anglePQO\$
6	Congruency	\$\triangleNQM \cong \trianglePQO\$
7	Prove that	Henced prove that \$\triangleNQM\$ and \$\cong\$ \$\trianglePQO\$ by the SAS congruence rule.

Steps

Statment

Solution

Given

Give that MNOP is a square, NP and MO are the diagonals of the square meets at a point Q.

Side of triangles

NQ = PQ and QM = QO

Angles

\$\angleNQM and \anglePQO\$

Since angles, \$angleNQM and \anglePQO\$ from a pair vertically opposite angles we have

\$\angleNQM and \anglePQO\$

Congruency

\$\triangleNQM \cong \trianglePQO\$

Prove that

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