Maths-
General
Easy
Question
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](data:image/png;base64,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)
The correct answer is: Hence proved
Solution :-
Aim :- Prove that ![A E squared plus B D squared equals A B squared plus D E squared](data:image/png;base64,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)
Hint :- Applying pythagoras theorem to both triangles ABC,DEC,DBC and AEC. find the equation, add them and substitute proper conditions to prove the condition
Explanation(proof ) :-
Applying pythagoras theorem to triangle ABC , we get
![A B squared equals A C squared plus B C squared minus bold Eql](data:image/png;base64,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)
Applying pythagoras theorem to triangle DEC , we get
— Eq2
Applying pythagoras theorem to triangle DBC , we get
![D B squared equals B C squared plus D C squared minus bold Eq 3](data:image/png;base64,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)
Applying pythagoras theorem to triangle AEC , we get
![A E squared equals A C squared plus E C squared minus bold Eq 4](data:image/png;base64,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)
![](data:image/png;base64,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)
Adding Eq 1 and 2,we get
![A B squared plus D E squared equals D C squared plus E C squared plus A C squared plus B C squared minus bold Eq 5](data:image/png;base64,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)
Adding 3 and 4 we get ,
![D B squared plus A E squared equals A C squared plus E C squared plus B C squared plus D C squared minus bold Eq bold 6](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAToAAAATCAYAAAAAlsEWAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAABIhJREFUeNrtWl9k1VEcP665Jolkcs2MzEwykWRmEpNJMmMySRJ7SA89jEkPPUwv6SFJzEwmM64kM3tJkqSXzPSQGcmespdJJlcut++xz62zs3N+5/zu/d1zz1nnw5f9fvs69/P9/M75nu/5w1hjUYH9JvtA1sXCQKi8o+6R9/8cQ9ORI7tJthJ5R/6Rd4xhv6MUeUf+kXeMYT/jLNm7yDvyj7xjDL5k8opg22RFss4E/zLZBtlXskWyguRTwLr/mMM4bqeMU9yjyHnMm4HPA7JVsl/QforscJN0t9HSV96mvhuC3qYx6ksMFYPVg0tkbxFbCd9yQOfcBSHE9ToP/BaEGTH4M4j3THjuJlvSdKBG4TIGWYtlnCr4yJtjArwGhCTSgQTZDN1ttAyFt9x3Q+BtGqM+xdCoRDeRts1hsnnN/0bJfkoztMp/RHjHBVsmO1SjKLWAz1CfyV6DX9o46+XNGsh7kmzGoi2Xupu0DIn3iPQuNL1VY9RFDGkTXZboFVYP4ygSePyDSNpK3EN21IGXyKcl/0nJZ45sCH9z4XrqEKUWTJONkV0je5IQ52RCG/XwZg3i3Y3lVYtFWy51N2kZEm+x7/rM23aMuoqhEYmunew5EncJyb2N7JPUxjSe76YhUsRaV4c3yJSi/zAy6EmyWWmPqZ7ytJZE1ydk8aP4yLo4h1OW2LWW45WMeD+03L9zrbtJS9956/quz7xtx6irGLJOdDyhfVfwWUPlJraxhuduxPsDiZHv1/XrfmDdsD7/BhKiv7ghOpSxKGnQgmzfIbxb0cxS65oP287cw5b3F+bmEmda3U1ahsBb1Xd95m07Rl3FkDbRmZLqY7zjWzkn8I4ftDxS+FcPZl5p2j0nk8jhg+twgGxT45/HLPIRmTVrEWxmAlVJf5/tXH5ME6dr2PDOscbda6pHd5OWIfBW9d1Q9RbHqI8x2Ppv4N0pi6qwjOcl4ft14rmCImIXzqDs1YHvHc0Y/K+wnSNs1zNdD1Pf5Ob3gRZTxumy49ryzmOvwtWsawuTliHxFvtuqHqLY9RlDFkvXcsWybKKLTy3Sn5H8H5Psh/DPoUOvIzsNfhfZXYnPFl3gPcJSUa+rmGK0yXS8N7GjO3TwLPRMhTect8NUW95jLqKIetEV12OtikqVrmNIp47NL57kj1fF1/X/PAjmMl/Fh/DZQcYV3ATsUB2wTJOl0jLe5Yln7Y1Y+DZaBkKb7nvhqa3aoy6iiHrRLcMv6KQ7PjBwqqijX4880vOx/GugPHD38v3ItlLtntDlpe+5/GjTxVkRH9OZhRE8g47QAGz2MEEnxtSB5DjbAZq4d2JMv0O+3ebnZfrF9GhB5sw8Gy09J23ru+GoLdpjLqKIattnir6NP9f0CTLKY3/pqLS+7vWrWCNzJ3m8aMqiP4lkHB9alnER0sC57Su4S1b3mPeHPwEbQ7lOOfLj9JfSJWfS9hq6TPvpL7rM2+bMepbDGn2snkSXsEWzhYm/daEqnAU/mXEOqtKchEREREhoFF3/CIiIiJioouIiIhwhRKr4X7gH93xrXFYj8nlAAABv3RFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT5EPC9taT48bXN1cD48bWk+QjwvbWk+PG1uPjI8L21uPjwvbXN1cD48bW8+KzwvbW8+PG1pPkE8L21pPjxtc3VwPjxtaT5FPC9taT48bW4+MjwvbW4+PC9tc3VwPjxtbz49PC9tbz48bWk+QTwvbWk+PG1zdXA+PG1pPkM8L21pPjxtbj4yPC9tbj48L21zdXA+PG1vPis8L21vPjxtaT5FPC9taT48bXN1cD48bWk+QzwvbWk+PG1uPjI8L21uPjwvbXN1cD48bW8+KzwvbW8+PG1pPkI8L21pPjxtc3VwPjxtaT5DPC9taT48bW4+MjwvbW4+PC9tc3VwPjxtbz4rPC9tbz48bWk+RDwvbWk+PG1zdXA+PG1pPkM8L21pPjxtbj4yPC9tbj48L21zdXA+PG1vPiYjeDIyMTI7PC9tbz48bWkgbWF0aHZhcmlhbnQ9ImJvbGQiPkVxPC9taT48bW4gbWF0aHZhcmlhbnQ9ImJvbGQiPjY8L21uPjwvbWF0aD7oCFXnAAAAAElFTkSuQmCC)
But substitute Eq6 in Eq5
We get ![A E squared plus B D squared equals A B squared plus D E squared](data:image/png;base64,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)
Hence proved
Related Questions to study
Maths-
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 ?
Maths-General
Maths-
In the given figure,
: 3. Find
.
![](data:image/png;base64,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)
In the given figure,
: 3. Find
.
![](data:image/png;base64,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)
Maths-General
Maths-
Maths-General
Maths-
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 ?
Maths-General
Maths-
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
.
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
.
Maths-General
Maths-
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?
Maths-General
Maths-
Maths-General
Maths-
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
Maths-General
Maths-
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?
Maths-General
Maths-
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
Maths-General
Maths-
In
and
. Hence find the measure of each angle
In
and
. Hence find the measure of each angle
Maths-General
Maths-
Benjamin fills his car with 50 litres of petrol. How much does it cost him if petrol is selling at 94.6pence per litre?
Benjamin fills his car with 50 litres of petrol. How much does it cost him if petrol is selling at 94.6pence per litre?
Maths-General
Maths-
Prove that △ CAB ≅△ CAD
![](data:image/png;base64,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)
Prove that △ CAB ≅△ CAD
![](data:image/png;base64,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)
Maths-General
Maths-
Maths-General
Maths-
Write the following in expanded fractional form :
d) 0.00016
Write the following in expanded fractional form :
d) 0.00016
Maths-General