SaiBook.us Geometry

Lesson Example Discussion Quiz: Class Homework

Step-4

Title:

Grade: 10-a Lesson: S2-L3

Explanation:

From the figure we can observe that
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SP and SR are the radius of the circle, SQ bisects \$\angle PSR\$ and \$PQS\$ and \begin{align} SP &= SR \tag{Given}\\ PQ &= RQ \tag{Given}\\ \end{align}

Consider \$\triangle PQS\$ and \$\triangle RQS\$.

\begin{align} QS &= QS \tag{Common side} \\ PQ &= RQ \tag{Given} \\ PS &= RS \tag{Given} \\ \end{align}

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

Henced proved that \$\trianglePQS\$ \$\cong\$ \$\triangleRQS\$ by the SSS congruence rule.

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Steps	Statment	Solution
1	Given	From the figure SP and SR are the radius of the circle, SQ bisects \$\angle PSR\$ and \$PQS\$ and
2	Side of triangles	SP = SR and PQ = RQ
3	Consider triangles	\$\triangle PQS and \triangle RQS\$
4	Common side	QS = QS
5	Side of triangles	PQ = RQ and PS = RS
6	So, Congruency	\$\triangle PQS \cong \triangle RQS\$
7	Prove that	Henced proved that \$\trianglePQS\$ \$\cong\$ \$\triangleRQS\$ by the SSS congruence rule.

Steps

Statment

Solution

Given

From the figure SP and SR are the radius of the circle, SQ bisects \$\angle PSR\$ and \$PQS\$ and

Side of triangles

SP = SR and PQ = RQ

Consider triangles

\$\triangle PQS and \triangle RQS\$

Common side

QS = QS

Side of triangles

PQ = RQ and PS = RS

So, Congruency

\$\triangle PQS \cong \triangle RQS\$

Prove that

Henced proved that \$\trianglePQS\$ \$\cong\$ \$\triangleRQS\$ by the SSS congruence rule.