9th Grade > Mathematics
CONSTRUCTIONS MCQs
Total Questions : 56
| Page 2 of 6 pages
Answer: Option B. -> False
:
B
Theperpendicular bisectoris a line that divides a line segment into two equal parts andalso makes a right angle with the line segment. Here CD divides AB into two equal parts but is not perpendicularto it. Hence it is not a perpendicular bisector.
:
B
Theperpendicular bisectoris a line that divides a line segment into two equal parts andalso makes a right angle with the line segment. Here CD divides AB into two equal parts but is not perpendicularto it. Hence it is not a perpendicular bisector.
Answer: Option A. -> 80∘
:
A
With a ruler and compass we can construct 15∘,30∘,45∘,60∘, 90∘,105∘angles. We cannot construct80∘.
:
A
With a ruler and compass we can construct 15∘,30∘,45∘,60∘, 90∘,105∘angles. We cannot construct80∘.
Answer: Option A. -> 80∘
:
A
The correct procedure to construct the given triangle is:
1. Draw the base BC of Δ ABC as given and construct ∠ XBC of the required measure at B as shown.
2. Keeping the compass at point B cut an arc from the ray BX such that its lengthequals to AB + AC at point P and join it to C as shown.
3. Now measure ∠BPC and from C draw an angle equal to ∠BPC as shown.
Thus, option A is correct.
:
A
The correct procedure to construct the given triangle is:
1. Draw the base BC of Δ ABC as given and construct ∠ XBC of the required measure at B as shown.
2. Keeping the compass at point B cut an arc from the ray BX such that its lengthequals to AB + AC at point P and join it to C as shown.
3. Now measure ∠BPC and from C draw an angle equal to ∠BPC as shown.
Thus, option A is correct.
:
75∘=90∘+60∘2
Hence bisecting 90∘ and 60∘will give 75∘.
Answer: Option B. -> False
:
B
To draw a triangle,we must know its perimeter along with twobase angles. Hence the given statement is false.
:
B
To draw a triangle,we must know its perimeter along with twobase angles. Hence the given statement is false.
Answer: Option A. -> Angle bisector
:
A
An angle bisector divides a given angle into two equal angles. Since BD divides ∠ ABC into two equal angles, it is an angle bisector.
:
A
An angle bisector divides a given angle into two equal angles. Since BD divides ∠ ABC into two equal angles, it is an angle bisector.
Question 18. The steps to draw a triangle with the base BC, a base angle ∠B and the difference of other two sides is given below.
1. Draw the base BC and at point B make an angle say XBC equal to the given angle.
2. Cut the line segment BD equal to AB - AC on the reflection of ray BX (i.e. BX').
3. Join DC and draw the perpendicular bisector, say PQ of DC.
The next step will be:
1. Draw the base BC and at point B make an angle say XBC equal to the given angle.
2. Cut the line segment BD equal to AB - AC on the reflection of ray BX (i.e. BX').
3. Join DC and draw the perpendicular bisector, say PQ of DC.
The next step will be:
Answer: Option A. -> True
:
A
It is possible to get 30∘from given angle of 60∘by simply drawing an angle bisector. Hence the given statement is true.
:
A
It is possible to get 30∘from given angle of 60∘by simply drawing an angle bisector. Hence the given statement is true.
Answer: Option B. -> 45∘
:
B
In ΔAXB
PQ is the perpendicular bisector ofXA, the two triangles formed are congruentby SASrule.
∴ AB = XB
⇒∠BAX=∠AXB
∠ABC=∠BAX+∠AXB
= 2∠AXB=∠LXY
[Since ∠AXB is angle bisector of ∠LXY]
Similarly,∠ACB=∠MYXTherefore,∠ABC=75∘and∠BCA=60∘InΔABC,wehave∠ABC+∠BCA+∠CAB=180∘75∘+60∘+∠CAB=180∘∠CAB=180∘−135∘∠CAB=45∘
:
B
In ΔAXB
PQ is the perpendicular bisector ofXA, the two triangles formed are congruentby SASrule.
∴ AB = XB
⇒∠BAX=∠AXB
∠ABC=∠BAX+∠AXB
= 2∠AXB=∠LXY
[Since ∠AXB is angle bisector of ∠LXY]
Similarly,∠ACB=∠MYXTherefore,∠ABC=75∘and∠BCA=60∘InΔABC,wehave∠ABC+∠BCA+∠CAB=180∘75∘+60∘+∠CAB=180∘∠CAB=180∘−135∘∠CAB=45∘
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