Lesson Example Discussion Quiz: Class Homework |
Step-5 |
Title: |
Grade: 10-a Lesson: S2-L1 |
Explanation: |
Given that a circle with center O and PR and QS are the diameters of the circle.
PR and QS intersect at O the center of the circle, the center of the circle O is also the mid-point for PR and QS.
From the figure we can observe that
\begin{align}
PR \bot QS \tag{Given} \\
PR = QS \tag{Given} \\
PO = SO \\
QO = RO \\
\end{align}
Consider \$\triangle POQ\$ and \$\triangle SOR\$
\begin{align} PO = SO \\ QO = RO \\ \end{align}
Since angles, \$\angle POQ\$ and \$\angle SOR\$ form a pair of vertically opposite angles, we have
\begin{align} \angle POQ = \angle SOR \\ \end{align}
Henced proved that \$\trianglePOQ\$ \$\cong\$ \$\triangleSOR\$ by the SAS congruence rule.
From the figure we can observe that
| Steps | Statment | Solution |
|---|---|---|
1 |
Given |
Given that a circle with center O and PR and QS are the diameters of the circle. |
2 |
Intersect points |
PR and QS intersect at O the center of the circle, the center of the circle O is also the mid-point for PR and QS. |
3 |
Side of triangles |
\$PR \bot QS\$ and PR = QS and PO = SO and QO = RO |
4 |
Consider Angles |
\$\anglePOQ and \angleSOR\$ |
5 |
Congruency |
\$\triangleCDB \cong \triangleADB\$ |
6 |
Sides |
PO = SO and QO = RO |
7 |
Since angles, \$\angle POQ\$ and \$\angle SOR\$ form a pair of vertically opposite angles, we have |
|
8 |
Angles |
\$\anglePOQ and \angleSOR\$ |
9 |
Prove that |
Henced proved that \$\trianglePOQ\$ \$\cong\$ \$\triangleSOR\$ by the SAS congruence rule. |
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