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Published on: 31/10/2025
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Questions + Answers key
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1.
Draw a rough sketch of two triangles such that they have three pairs of congruent parts but still the triangles are not congruent.
2.
In the given figure, ΔPQR is a right angled at P, V and T are the points on line QRT, if QP II ST and US II RP, find ㄥS.
3.
In each of the given pairs of triangles of figure using only RHS congruence rule. Determine which pairs of triangles are congruent? In case of congruence, write the result in symbolic form.
4.
A chocolate is in the form of a quadrilateral with sides 6 cm, 10 cm, 5 cm and 5 cm. It is cut into two parts along one of its diagonals by a lady. Part I is given to her maid and part II is equally divided among her driver and rnali.
What value is depicted by lady in distribution of chocolate in two parts?
5.
A chocolate is in the form of a quadrilateral with sides 6 cm, 10 cm, 5 cm and 5 cm. It is cut into two parts along one of its diagonals by a lady. Part I is given to her maid and part II is equally divided among her driver and maid.
Use congruence of triangle rule and cheek is this distribution fair or not.
6.
In the following figure, ΔABC and ΔDCB are right angled at A and D respectively and AC = DB. Prove that ΔABC ≌ ΔDCB.
7.
Is the perimeter of two congruent triangles is equal? Justify your answer.
8.
If ΔABC ≅ ΔPQR, where ㄥA=(3x-10) and ㄥP=(x+50), then the value of ㄥC, where ㄥC=x.
9.
Which of the following pair of figures are congruent?
10.
Which of the following pair of figures are congruent?
1.
In some special cases (which depend on the lengths of the sides and the size of the angle involved), SSA is enough to show congruence. However, it is not always enough.
Consider the following triangles :
Here side AB is congruent to side DE (S) side AC is congruent to side DF (S) angle C is congruent to angle F (A)
But the triangles are not congruent, as we can see.
What happens is this : If we draw a vertical line through point A in the first triangle, we can sort of "flip" side AB around this line to get the second triangle, If we were to lay one triangle on top of the other and draw the vertical line, this how it would look.
Clearly, side DE is just side AB flipped around the line. So, we have not changed the length of the side, and the other side AC (or DF) is unchanged, as is angle C (or F). So, these two triangles that have the same SSA information, but they are not congruent.
2.
Given ㄥQPR = 90°, ORT is a line, OP II ST and US II PR, ㄥS=?
Now, we extend US up to U such that it intersects QP at U.
PR || US [given]
⇒ PR || U'S, U'P is a transversal.
So, ㄥP + ㄥU' = 180° [by the property, sum of two interior angles on the same side of a transversal]
900 + ㄥU = 180°
ㄥU' = 180° - 90°
ㄥU = 90°
Similarly, OP II ST [given]
Then, US is a transversal.
So, ㄥU' + ㄥS =180° ⇒ 90° + ㄥS =180°
⇒ ㄥS=1800 - 90° ⇒ ㄥS = 90°.
3.
In ΔXYZ and ΔUZY, XZ =UY [given]
YZ = YZ [common]
ㄥXYZ = ㄥUZY [90° each]
So, by RHS congruence rule, two triangles are congruent.
The correspondence is ㄥX ↔️ ㄥU, ㄥY ↔️ ㄥZ and ㄥZ ↔️ ㄥY
In symbolic form, ΔXYZ ≅ ΔUZY
4.
According to the question, we have following figure:
She was partial to her servants.
So, distribution of chocolate was not fair.
5.
According to the question, we have following figure:
Quadrilateral ABCD can be divided into two triangles i.e. ΔABD and ΔBDC.
In two triangles,
AD ≠ CD
AB ≠ BC
BD = BD [common side]
So, ΔABD ≅ ΔBCD are not true.
6.
In the given figure, we have
ㄥA = 900 [right angled at A]
ㄥD = 900 [right angled at D]
∴ ㄥA = ㄥD
BC = BC [common side]
Also, AC = DB [given]
So by RHS congruence criterion ΔABC and ΔDCB are congruent to each other.
∴ ΔABC ≅ ΔDCB
7.
Do yourself
8.
ㄥC = x =300
9.
Congruent
10.
Not congruent
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