Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Offsite Campus Turito Championship

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Maths-

General

Easy

Question

$A B C D text is a rhombus, prove that end text A C squared plus B D squared equals 4 times A B squared$

hint Hint:

Hint :- Applying pythagoras theorem to both triangles AIB. find the AB2 and multiply by 4 and substitute proper conditions to prove the condition .

The correct answer is: Hence proved .

Aim :- Prove that $A C squared plus B D squared equals 4 times A B squared$
Explanation(proof ) :-
Given ABCD is a rhombus
The diagonals in the rhombus are perpendicular bisectors.
BI = $1 half$ BD — Eq 1
AI = $1 half$ AC — Eq 2
Applying pythagoras theorem in ΔAIB,
$A B squared equals A I squared plus B I squared$

Multiplying with 4 on both sides
$4 A B squared equals 4 A I squared plus 4 B I squared not stretchy rightwards double arrow 4 times A B squared equals left parenthesis 2 A I right parenthesis squared plus left parenthesis 2 B I right parenthesis squared$
Applying Eq 1 and 2
We get, $text 4. end text A B squared equals A C squared plus B D squared$
Hence proved .

Related Questions to study

In $straight triangle ABC$ , DA = DB = DC. Show that $straight angle ACB equals 90 to the power of ring operator$ .

In $straight triangle ABC$ , DA = DB = DC. Show that $straight angle ACB equals 90 to the power of ring operator$ .

In the figure, if $Q T perpendicular P R comma straight angle T Q R equals 40 to the power of ring operator$ and $straight angle S P R equals 30 to the power of ring operator$ find x and y.

In the figure, if $Q T perpendicular P R comma straight angle T Q R equals 40 to the power of ring operator$ and $straight angle S P R equals 30 to the power of ring operator$ find x and y.

Would you classify the number 200 as a perfect square , a perfect cube , both or neither ?

Would you classify the number 200 as a perfect square , a perfect cube , both or neither ?

parallel

$text In an isosceles Triangle end text A B C comma A B equals A C text and end text D text is a point on end text B C text produced. Prove that end text A D squared equals A C squared plus B D. C D$

$text In an isosceles Triangle end text A B C comma A B equals A C text and end text D text is a point on end text B C text produced. Prove that end text A D squared equals A C squared plus B D. C D$

D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C . Prove that
$A E squared plus B D squared equals A B squared plus D E squared$

D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C . Prove that
$A E squared plus B D squared equals A B squared plus D E squared$

A square technology chip has an area of 25 square centimetres. How long is each side of the chip ?

A square technology chip has an area of 25 square centimetres. How long is each side of the chip ?

parallel

In the given figure, $straight angle straight B colon straight angle straight C equals 2$ : 3. Find $straight angle straight B$ .

In the given figure, $straight angle straight B colon straight angle straight C equals 2$ : 3. Find $straight angle straight B$ .

$text In Triangle end text A B C comma straight angle B equals 90 to the power of ring operator text and end text D text is a point on end text B C text . Prove that end text A D squared plus B C squared equals A C squared plus B D squared$

$text In Triangle end text A B C comma straight angle B equals 90 to the power of ring operator text and end text D text is a point on end text B C text . Prove that end text A D squared plus B C squared equals A C squared plus B D squared$

Would you classify the number 169 as a perfect square , a perfect cube , both or neither ?

Would you classify the number 169 as a perfect square , a perfect cube , both or neither ?

parallel

A farmer has a square plot of land, where he wants to grow five different crops at a time. One-half of the area in the middle, he wants to grow wheat but in rest of the four equal triangular parts, he wants to grow different crops. p and q are the mid-points of sides CA and CB respectively of a triangular part ABC right-angled at c . Prove that $4 open parentheses A Q squared plus B P squared close parentheses equals 5 A B squared$ .

A farmer has a square plot of land, where he wants to grow five different crops at a time. One-half of the area in the middle, he wants to grow wheat but in rest of the four equal triangular parts, he wants to grow different crops. p and q are the mid-points of sides CA and CB respectively of a triangular part ABC right-angled at c . Prove that $4 open parentheses A Q squared plus B P squared close parentheses equals 5 A B squared$ .

A trophy store wishes to make brass medallions, each of mass 17.5 g, from 140 kg of brass. How many medallions can be made?

A trophy store wishes to make brass medallions, each of mass 17.5 g, from 140 kg of brass. How many medallions can be made?

$B D text is an altitude of the triangle end text A B C text . Prove that end text A C left parenthesis A D minus D C right parenthesis equals A B squared minus B C squared$

$B D text is an altitude of the triangle end text A B C text . Prove that end text A C left parenthesis A D minus D C right parenthesis equals A B squared minus B C squared$

parallel

A large mixer at a bakery holds 0.75 tonnes of dough. How many bread rolls, each of mass 150 g,can be made from the dough in the mixer

A large mixer at a bakery holds 0.75 tonnes of dough. How many bread rolls, each of mass 150 g,can be made from the dough in the mixer

What is the special case when SSA condition works to
prove the triangle congruence? What do the sides and the angle represent
that case?

What is the special case when SSA condition works to
prove the triangle congruence? What do the sides and the angle represent
that case?

If two sides and the included angle of one triangle are
congruent to two sides and the included angle of a second triangle, then the
two triangles are congruent by

If two sides and the included angle of one triangle are
congruent to two sides and the included angle of a second triangle, then the
two triangles are congruent by

parallel

card img

With Turito Academy.

card img

With Turito Foundation.

card img

Get an Expert Advice From Turito.

Turito Academy

card img

With Turito Academy.

Test Prep

card img

With Turito Foundation.