DAV Class 7 Maths Chapter 9 Worksheet 1
Congruent Triangles Worksheet 1
1. Fill in the blanks so as to make a true statement.
(i) Two line segments are congruent, if they have the same length
(ii) Two angles are congruent, if they have the same measure
(iii) Two squares are congruent, if they have the same side length
(iv) Two circles are congruent, if they have the same radius
(v) Two rectangles are congruent, if they have the same length and same breadth
2. In the diagrams below, state which pairs of triangles are congruent by SSS congruence condition. If congruent, write the congruence of triangles in symbolic form.
(i)
Solution
\[ \begin{align*} \text{In } \triangle ABC & \text{ and } \triangle PQR \\ \text{AB} &= \text{QR} \implies 2 \, cm \\ \text{BC} &= \text{RP} \implies 3 \, cm \\ \text{AC} &= \text{QP} \implies 2.5 \, cm \\ \\ \text{By SSS} & \text{ congruence condition,} \\ & \triangle ABC \cong \triangle QRP \end{align*} \]
Answer \( \color{red} \triangle ABC \cong \triangle QRP \)
(ii)
Solution
\[ \begin{align*} \text{In } \triangle PQS & \text{ and } \triangle PRS \\ \text{PQ} &= \text{PR} \implies 3.5 \, cm \\ \text{QS} &= \text{RS} \implies 2 \, cm \\ \text{SP} &= \text{SP} \implies 2.5 \, cm \\ \\\text{By SSS} & \text{ congruence condition,} \\ & \triangle PQS \cong \triangle PRS \end{align*} \]
Answer \( \color{red} \triangle PQS \cong \triangle PRS \)
(iii)
Solution
\[ \begin{align*} \text{In } \triangle ABD & \text{ and } \triangle FEC \\ \text{AB} &= \text{FE} \implies 3 \, cm \\ \text{BD} &= \text{EC} \implies 3 \, cm \\ \text{DA} &= \text{CF} \implies 5.5 \, cm \\ \\\text{By SSS} & \text{ congruence condition,} \\ & \triangle ABD \cong \triangle FEC \end{align*} \]
Answer \( \color{red} \triangle ABD \cong \triangle FEC \)
(iv)
Solution
\[ \begin{align*} \text{In } \triangle POQ & \text{ and } \triangle ROS \\ \text{PO} &= \text{RO} \implies 3 \, cm \\ \text{OQ} &= \text{OS} \implies 4 \, cm \\\text{Third side} & \text{ not given.} \end{align*} \]
Answer Triangles are \( \color{red} \text{Not congruent} \) by SSS condition.
3. In the diagram below, PS = RS and PQ = RQ
(i) Is \( \triangle PQS \cong \triangle RQS \) ?
Answer \( \color{red} Yes \) , by SSS congruence condition.
(ii) State the three pairs of matching parts you have used to answer (i).
Answer
\[ \begin{align*} \text{In } \triangle PQS & \text{ and } \triangle RQS \\ \text{PS} &= \text{RS} \text{ (Given)} \\ \text{PQ} &= \text{RQ} \text{ (Given)} \\ \text{SQ} &= \text{SQ} \text{ (Common side)} \\ \\\text{By SSS} & \text{ congruence condition,} \\ & \triangle PQS \cong \triangle RQS \end{align*} \]
(iii) \( \angle P = \) \( \color{red} \angle R \)
4. In the diagram below, △ABC is isosceles with AB = AC. D is the mid-point of base BC.
(i) Is \( \triangle ADB \cong \triangle ADC \) ? If yes, by which congruence condition?
Answer \( \color{red} Yes \), by SSS congruence condition.
(ii) State the three pairs of matching parts that you use to arrive at your answer.
Answer
\[ \begin{align*} \text{In } \triangle ADB & \text{ and } \triangle ADC \\ \text{AB} &= \text{AC} \text{ (Given)} \\ \text{BD} &= \text{CD} \text{ ( D is the mid point of BC)} \\ \text{AD} &= \text{AD} \text{ (Common side)} \\ \\\text{By SSS} & \text{ congruence condition,} \\ & \triangle ADB \cong \triangle ADC \end{align*} \]
5. In △PQR and △XYZ, PQ = XZ and OR = YZ as shown in the diagram. What additional information is required to make the two triangles congruent by SSS congruence condition?
Answer
In △PQR and △XYZ. \(\color{red} PR = XY \), is required to make the two triangles congruent by SSS congruence condition.
6. If \( \triangle ABC \cong \triangle DEF \), fill in the blanks to make each statement true.
(i) AB = DE
(ii) \( \angle C = \) \( \angle F \)
(iii) EF = BC
(iv) \( \angle D = \) \( \angle A \)
(v) CA = FD
(vi) \( \angle B = \) \( \angle E \)