ADDITIONAL QUESTIONS AND ANSWERS
1). If ∆ LMN ∆ PRQ, Write the part (s) of ∆ PRQ that corresponds to
i) LN ii) ∠ N iii) ∠ L iv) LM v) MN
Ans: i) PQ ii) ∠ R iii) ∠ P iv) PR v) RQ
2). If ∆ HIJ ≅ ∆ FED under the correspondence HIJ ↔ FED write all the corresponding congruent parts of the triangles.
Ans: Angles
∠H ↔ ∠F, ∠I ↔ ∠E, ∠J ↔ ∠D
HI ↔ FE, IJ ↔ ED, HJ ↔ FD
3). Examine whether the given triangles are congruent or not.
Ans: BC = DF = 3.5 cm
AB = DE = 3cm
AC = EF = 3.5cm
∴ ∆ LMN ≅ SRT by S.S.S Congruence Criteria
4). In the adjoining figure PR = PQ and O is the mid-point of QR
1. State the three pairs of equal parts in ∆ PSQ and ∆ PSR
Ans: PQ = PR Given
QS = RS Since S is the mid-point
SP = PS common side
ii) Is ∆ PSQ ≅ ∆ PSR? Give reason
Ans: Yes. ∆ PSQ ≅ ∆ PSR by S.S.S congruence criteria.
iii) Is ∠Q = ∠R. Why?
Ans: Yes∠Q = ∠R by corresponding parts of congruent triangles.
5). In the adjoining figure, MO = NL and ML = NO. Which of the following statements is meaningfully written.
i) ∆ MNO ≅ ∆ MNL ii) ∆ MNO ≅ ∆ NML
Ans: MO = NL (Given)
LM = NO (Given)
MN = MN (Common side)
∴ ∆ MNL ≅ ∆ NML ∆ MNO ≅ ∆ NML is not meaningfully written.
6). By applying S.A.S congruence rule, you want to establish that ∆PQR ≅ ∆ FED. If it is given that PQ = FE And RP = DF.
What additional information is needed to establish the congruence?
Ans: Let us draw the figure of ∆ PQR ≅ ∆ FED
PQ = FE Given
RP = DE
To make S.A.S Congruence true, it is required to have
∠QRP = ∠ EFD
7). In the adjoining figure AB and CD bisect each other at O
i) State the three pairs of equal parts in two triangles ΔAOC andΔ BOD
(pic)
Ans: AO = BO (From the given figure)
CO = DO (From the given figure)
∠AOC = ∠BOD (Vertically opposite angle)
8). Which of the following statements are true?
a) ∆ AOC ≅ ∆ DOB
b) ∆ AOC ≅ ∆ BOD
Ans: ∆ AOC ≅ ∆ BOD
Since AD = BD
∠AOB = ∠ BOD
OC = OB ∴ Statement ( a) is true.
9). In the adjoining figure BD and CE are altitudes of ∆ ABC such that BD = CE. (fig)
i) State the three pairs of equal parts in ∆ CBD and ∆ BCE
Ans:
i) BD = CE (Given)
ii) ∠ BDE = ∠ CEB (Each is 90°)
iii) BC = BC ( Common side)
ii) Is ∆ CBD ≅ ∆ BCE? Why or why not?
Ans: Yes CBD ≅ ∆ BCE
Since BD = CE (given)
∠ BDC = ∠ CED (each is 90°)
BC = BC (Common side)
∴ ∆ CBD ≅ ∆ BCE R.H.S congruence criteria
iii) Is ∠ DCB = ∠ EBC
Ans. Yes, by corresponding parts of congruent triangles
10). In the given congruent triangles under A.S.A, fine the value of x and y, ∆PQR = ∆ STU
Ans: ∆ PQR ≅ ∆ STU (Given)
i) ∴∠R = ∠ U (By A.S.A rule)
∴ Z = 30°
ii) By angle sum property of a triangle In ∆ STU we get
x + 60° + Z = 180°
x + 60° + 30° = 180°
x + 90° = 180° ∴ x = 180° – 90° ∴ x = 90°
11). In the adjoining figure, say AZ bisects ∠DAB as well as ∠DCB.
i) State the three pairs of equal parts in triangles ΔBAC and ΔDAC
Ans: ∠DAC = ∠BAC ( Ray AZ bisects ∠DAB)
∠DAC = ∠BCA (Ray AZ bisects ∠CB)
AC = AC Common side
ii) Is ∆BAC ≅ ∆ DAC. Give reasons
Ans: Yes, ∆ BAC ≅ ∆ DAC (By A.S.A Congruence criteria)
iii) Is AB = AD.
Ans: Yes. AB = AD (by corresponding parts of congruent triangles).
iv) Is CD = CB.
Ans: Yes CD = CB (by corresponding parts of congruent triangles).