9th Grade > Mathematics
TRIANGLES MCQs
Total Questions : 56
| Page 2 of 6 pages
Answer: Option B. -> BC
:
B
Sum of all angles in a triangle is 180∘.
∠BAC + ∠CAB + ∠CBA = 180∘
∠BAC + 30∘ +45∘ =180∘
∠BAC = 180∘−(30∘+45∘)=105∘.
The side opposite to the largest angle will be the longest.
Side opposite to ∠BAC = BC.
Hence, BC is the longest side.
:
B
Sum of all angles in a triangle is 180∘.
∠BAC + ∠CAB + ∠CBA = 180∘
∠BAC + 30∘ +45∘ =180∘
∠BAC = 180∘−(30∘+45∘)=105∘.
The side opposite to the largest angle will be the longest.
Side opposite to ∠BAC = BC.
Hence, BC is the longest side.
Answer: Option A. -> True
:
A
ConciderΔAOB,ΔAOCandΔBOC.AB=BC=AC(Sides of equilateral triangle)AO=BO=CO(Radii of circumcircle)∴ΔAOB≅ΔBOC≅ΔCOB(SSS congruence).∴Area ofΔAOB=Area ofΔBOC=Area ofΔAOC.ButArea ofΔAOB+Area ofΔBOC+Area ofΔAOC=Area ofΔABC.∴Area ofΔBOC=13Area ofΔABC
Hence, the given statement is true.
:
A
ConciderΔAOB,ΔAOCandΔBOC.AB=BC=AC(Sides of equilateral triangle)AO=BO=CO(Radii of circumcircle)∴ΔAOB≅ΔBOC≅ΔCOB(SSS congruence).∴Area ofΔAOB=Area ofΔBOC=Area ofΔAOC.ButArea ofΔAOB+Area ofΔBOC+Area ofΔAOC=Area ofΔABC.∴Area ofΔBOC=13Area ofΔABC
Hence, the given statement is true.
Answer: Option B. -> SAS
:
B
In △ACD and△ABD
∠BAD=∠CAD
[∵ AD is the bisector of ∠A]
AD = AD [common side]
AB = AC [Given]
△ACD≅△ABD [SAS congruency]
The triangles are congruent by SAS congruence rule.
:
B
In △ACD and△ABD
∠BAD=∠CAD
[∵ AD is the bisector of ∠A]
AD = AD [common side]
AB = AC [Given]
△ACD≅△ABD [SAS congruency]
The triangles are congruent by SAS congruence rule.
Answer: Option A. -> True
:
A
If all the sides of △CAT are equal to corresponding sides of △RAT, then △RAT will be congruent to △CAT and the congruence criterion will be SSS.
:
A
If all the sides of △CAT are equal to corresponding sides of △RAT, then △RAT will be congruent to △CAT and the congruence criterion will be SSS.
Answer: Option D. -> Any two sides of Δ1 and the included angle should be equal to any two sides and the included angle of Δ2
:
D
Two triangles can't be congruent if any twosides and oneangle of one are equal to any twosides and oneangle of the other.
They will be congruent when the angle is included between the equal pair of sides. This is the SAS condition of congruency of triangles.
The SAS congruence rule states:
Two triangles are congruent if two sides and the included angle of one triangle are equal to the two sides and the included angle of the other triangle.
:
D
Two triangles can't be congruent if any twosides and oneangle of one are equal to any twosides and oneangle of the other.
They will be congruent when the angle is included between the equal pair of sides. This is the SAS condition of congruency of triangles.
The SAS congruence rule states:
Two triangles are congruent if two sides and the included angle of one triangle are equal to the two sides and the included angle of the other triangle.
Answer: Option B. -> AB = DC
:
B
In △ACB and △CAD,
AD=BC [Given]
∠CAD=∠ACB [Alternate angles]
CA=AC [common side]
△ACB≅△CAD [SAS congruency]
∴AB=DC [CPCT]
:
B
In △ACB and △CAD,
AD=BC [Given]
∠CAD=∠ACB [Alternate angles]
CA=AC [common side]
△ACB≅△CAD [SAS congruency]
∴AB=DC [CPCT]
:
In the given figure,AD=AB(Given)DC=BC(Given)ACis common∴ΔADC≅ΔABC(SSS congruence)Hence,∠ACD=∠ACB=30∘
Answer: Option B. -> False
:
B
ConsiderΔABDandΔCDB,AB=CD(Opposite sides of parallelogram)AD=CB(Opposite sides of parallelogram)∠ABD=∠CDB(Alternate angles).∴ΔABD≅ΔCDB
Hence, the given statement is false as the vertices are not given in corresponding sequence in question.
:
B
ConsiderΔABDandΔCDB,AB=CD(Opposite sides of parallelogram)AD=CB(Opposite sides of parallelogram)∠ABD=∠CDB(Alternate angles).∴ΔABD≅ΔCDB
Hence, the given statement is false as the vertices are not given in corresponding sequence in question.
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