Maths-
General
Easy
Question
The perpendicular bisectors of the sides of a triangle ABC meet at point I. prove that IA=IB=IC
Hint:
Find the congruence rules used and thus find the equal sides.
The correct answer is: IA = IB = IC
![](data:image/png;base64,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)
In ΔABC, in which AD is perpendicular bisector of BC
BE is perpendicular bisector of CA
CF is perpendicular bisector of AB
AD, BE and CF meet at I
To prove IA=IB=IC
In ΔBID and ΔCID
BD = DC (given)
(AD is perpendicular bisector of BC)
ID = ID (common)
Hence by SAS congruence rule, we have
ΔBID ⩭ ΔCID
So, IB = IC (Corresponding part of congruent triangle)
Similarly, In ΔCIE and ΔAIE
CE = AE (given)
(BE is perpendicular bisector of AC)
IE = IE (common)
By SAS congruence rule, ΔCIE ⩭ ΔAIE
IC = IA (Corresponding part of congruent triangle)
Thus, IA = IB = IC
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Maths-General
Maths-
In Triangle ABC , AB= AC, and D is a point on AB. Such that AD=DC=BC. Show that ![straight angle B A C equals 36 to the power of ring operator](data:image/png;base64,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)
In Triangle ABC , AB= AC, and D is a point on AB. Such that AD=DC=BC. Show that ![straight angle B A C equals 36 to the power of ring operator](data:image/png;base64,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)
Maths-General
Maths-
In the triangle ABC, the angles at A and C are 40° and 95° respectively. If N is the foot of the perpendicular from C to AB , prove that CN = BN.
In the triangle ABC, the angles at A and C are 40° and 95° respectively. If N is the foot of the perpendicular from C to AB , prove that CN = BN.
Maths-General
Maths-
Given XYZ is a triangle in which XW is the bisector of the angle x and XW ⊥ yz. Prove that xy= xz.
Given XYZ is a triangle in which XW is the bisector of the angle x and XW ⊥ yz. Prove that xy= xz.
Maths-General
Maths-
ABC is a triangle in which altitudes BE and CF to sides AC and AB respectively are equal. Show that
(i) ΔABE ⩭ ΔACF
(ii) AB = AC
ABC is a triangle in which altitudes BE and CF to sides AC and AB respectively are equal. Show that
(i) ΔABE ⩭ ΔACF
(ii) AB = AC
Maths-General
Maths-
In the figure, OA = OD and OB = OC. Show that:
(i) AOB ⩭ DOC
(ii) AB || CD
![](data:image/png;base64,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)
In the figure, OA = OD and OB = OC. Show that:
(i) AOB ⩭ DOC
(ii) AB || CD
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)
Maths-General
Maths-
If AD ⟂ CD and BC ⟂ CD , AQ = PB and DP = CQ. Prove that ![straight angle D A Q equals straight angle C B P](data:image/png;base64,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)
![](data:image/png;base64,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)
If AD ⟂ CD and BC ⟂ CD , AQ = PB and DP = CQ. Prove that ![straight angle D A Q equals straight angle C B P](data:image/png;base64,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)
![](data:image/png;base64,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)
Maths-General
Maths-
Prove that the medians bisecting the equal sides of an isosceles triangle are also equal. If OA = OB and OD = OC, show that:
(i) AOD ⩭ BOC
(ii) AD || BC
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)
Prove that the medians bisecting the equal sides of an isosceles triangle are also equal. If OA = OB and OD = OC, show that:
(i) AOD ⩭ BOC
(ii) AD || BC
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)
Maths-General
Maths-
Kumar wants to spread a carpet on the floor of his classroom. The floor is a square
with an area of 4160.25 square feet. What is the length of carpet on each side?
Kumar wants to spread a carpet on the floor of his classroom. The floor is a square
with an area of 4160.25 square feet. What is the length of carpet on each side?
Maths-General
Maths-
The volume of a cubical box is 12167 cm3. Find the side of the box and its 6 sides area?
The volume of a cubical box is 12167 cm3. Find the side of the box and its 6 sides area?
Maths-General
Maths-
The area of a square is 289 m2, find its perimeter?
The area of a square is 289 m2, find its perimeter?
Maths-General
Maths-
What is the least seven digits which is a perfect square. Also find the square root of the number so obtained
What is the least seven digits which is a perfect square. Also find the square root of the number so obtained
Maths-General
Maths-
Find the least number which must be subtracted from 23416 to make it a perfect square.
Find the least number which must be subtracted from 23416 to make it a perfect square.
Maths-General