ABC is a triangle right angled at C as shown in the figure below. Which one of the following is correct?
AQ 2+ BP 2= AB 2+ PQ 2
Formula Used:
AC 2 = AB 2 + BC 2 (Pythagoras theorem)
Calculation:
In triangle AQC
Using above theorem
AQ 2= AC 2+ QC 2
Similarly
In triangle PBC
PB 2= PC 2+ BC 2
Adding both the equations
⇒ AQ 2+ BP 2= (AC 2+ BC 2) + (PC 2+ QC 2)
In triangle ABC and PQC
⇒ AB 2= AC 2+ BC 2and PQ 2= PC 2+ QC 2
Substituting back in the equation
⇒ AQ 2+ BP 2= AB 2+ PQ 2
∴ Correct answer is option 3)
Similar Questions
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1. The perimeter of a triangle is greater than the sum of its three medians.
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Important Questions from Triangles, Congruence and Similarity
In a $\Delta ABC$, $\angle C = (9/4) \angle B = (3/2) (\angle A+\angle B)$. Find the measure of the angles.
- The areas of two similar triangles $\Delta$XYZ and $\Delta$LMN are 49 cm$^2$ and 9 cm$^2$, respectively. If LM = 9 cm, then the length of XY is:
Triangles \(PQR\) and \(ABC\) are similar triangles. Triangle \(ABC\) have the following sides
\(AB = 12 \text{ cm}\),
\(AC = 15 \text{ cm}\),
\(CB = 21 \text{ cm}\).
Triangle \(PQR\) have the following sides:
\(PQ = 4 \text{ cm}\),
\(RQ = 7 \text{ cm}\).
What is the length of side \(PR\)?
For a pair of similar triangles, the angles made at \(Q\) is same in both the triangles \(PQR\) and \(LQJ\).
If the length of side \(QJ\) is 10 cm and \(QR\) is 5 cm, what is the ratio of their total areas?- In $\Delta ABC$ $\overline{PQ} \parallel \overline{AB}$. P and Q are on BC and CA respectively. If CQ : QA = 1 : 3 and CP = 4, then what is the value of BC?
