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

$\begin{aligned} In △ A B C & and △ P Q R \\ AB & = QR ⟹ 2 c m \\ BC & = RP ⟹ 3 c m \\ AC & = QP ⟹ 2.5 c m \\ By SSS & congruence condition, \\ △ A B C ≅ △ Q R P \end{aligned}$

Answer $△ A B C ≅ △ Q R P$

(ii)

Solution

$\begin{aligned} In △ P Q S & and △ P R S \\ PQ & = PR ⟹ 3.5 c m \\ QS & = RS ⟹ 2 c m \\ SP & = SP ⟹ 2.5 c m \\ By SSS & congruence condition, \\ △ P Q S ≅ △ P R S \end{aligned}$

Answer $△ P Q S ≅ △ P R S$

(iii)

Solution

$\begin{aligned} In △ A B D & and △ F E C \\ AB & = FE ⟹ 3 c m \\ BD & = EC ⟹ 3 c m \\ DA & = CF ⟹ 5.5 c m \\ By SSS & congruence condition, \\ △ A B D ≅ △ F E C \end{aligned}$

Answer $△ A B D ≅ △ F E C$

(iv)

Solution

$\begin{aligned} In △ P O Q & and △ R O S \\ PO & = RO ⟹ 3 c m \\ OQ & = OS ⟹ 4 c m \\ Third side & not given. \end{aligned}$

Answer Triangles are $Not congruent$ by SSS condition.

3. In the diagram below, PS = RS and PQ = RQ

(i) Is $△ P Q S ≅ △ R Q S$ ?

Answer $Y e s$ , by SSS congruence condition.

(ii) State the three pairs of matching parts you have used to answer (i).

Answer

$\begin{aligned} In △ P Q S & and △ R Q S \\ PS & = RS (Given) \\ PQ & = RQ (Given) \\ SQ & = SQ (Common side) \\ By SSS & congruence condition, \\ △ P Q S ≅ △ R Q S \end{aligned}$

(iii) $∠ P =$ $∠ R$

4. In the diagram below, △ABC is isosceles with AB = AC. D is the mid-point of base BC.

(i) Is $△ A D B ≅ △ A D C$ ? If yes, by which congruence condition?

Answer $Y e s$ , by SSS congruence condition.

(ii) State the three pairs of matching parts that you use to arrive at your answer.

Answer

$\begin{aligned} In △ A D B & and △ A D C \\ AB & = AC (Given) \\ BD & = CD ( D is the mid point of BC) \\ AD & = AD (Common side) \\ By SSS & congruence condition, \\ △ A D B ≅ △ A D C \end{aligned}$

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.
$P R = X Y$ , is required to make the two triangles congruent by SSS congruence condition.

6. If $△ A B C ≅ △ D E F$ , fill in the blanks to make each statement true.

(i) AB = DE

(ii) $∠ C =$ $∠ F$

(iii) EF = BC

(iv) $∠ D =$ $∠ A$

(v) CA = FD

(vi) $∠ B =$ $∠ E$

DAV Class 7 Maths Chapter 9 Worksheet 1

Congruent Triangles Worksheet 1

1. Fill in the blanks so as to make a true statement.

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.

3. In the diagram below, PS = RS and PQ = RQ

4. In the diagram below, △ABC is isosceles with AB = AC. D is the mid-point of base BC.

6. If △ABC≅△DEF, fill in the blanks to make each statement true.

6. If $△ A B C ≅ △ D E F$ , fill in the blanks to make each statement true.