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If in two right triangles, one of the ac...

If in two right triangles, one of the acute angles of one triangle is equal to an acute angle of the other triangle. Can you say that two triangles will be similar? Why?

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To determine whether the two right triangles are similar based on the information given, we can follow these steps: ### Step-by-Step Solution: 1. **Identify the Triangles**: Let's denote the first triangle as \( \triangle ABC \) where \( \angle B \) is the right angle, and the second triangle as \( \triangle PQR \) where \( \angle Q \) is the right angle. 2. **Acute Angles**: Since both triangles are right triangles, they each have two acute angles. We know that one acute angle of triangle \( ABC \) is equal to one acute angle of triangle \( PQR \). Let's denote this angle as \( \angle A \) in triangle \( ABC \) and \( \angle P \) in triangle \( PQR \). Thus, we have: \[ ...
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NCERT EXEMPLAR-TRIANGLES-Triangles
  1. Is the following statement true? Why? "Two quadrilaterals are similar,...

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  2. Two sides and the perimeter of one triangle are respectively three tim...

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  3. If in two right triangles, one of the acute angles of one triangle is ...

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  4. The ratio of the corresponding altitudes of two similar triangles is 3...

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  5. D is a point on side QR of DeltaPQR such that PDbotQR. Will it be corr...

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  6. In figure, if angleD=angleC, then it is true that DeltaADE~DeltaACB? W...

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  7. Is it true to say that, if in two triangles, an angle of one triangle ...

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  8. In P Q R ,\ \ Q M|P R and PR^2-P Q^2=Q R^2.Prove that Q M^2=P MxxM R

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  9. Find the value of x for which DEabs()AB in given figure.

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  10. In figure, if angle1=angle2 and DeltaNSQ=DeltaMTR, then prove that Del...

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  11. Diagonals of a trapezium PQRS intersect each other at the point 0 ,PQa...

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  12. In figure , if ABabs()DC and AC, PQ intersect each other at the point ...

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  13. Find the altitude of an equilateral triangle of side 8 cm.

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  14. If DeltaABC~DeltaDEF, AB=4cm, DE=6,EF=9 cm and FD=12 cm, then find the...

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  15. In figure, if DEabs()BC, then find the ratio of ar (DeltaADE) and ar(D...

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  16. ABCD is a trapezium in which ABabs()DC and P,Q are points on AD and BC...

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  17. Corresponding sides of two triangles are in the ratio 2\ :3 . If th...

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  18. In a Delta PQR, N is a point on PR, such that QNbotPR. If PNcdotNR=QN^...

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  19. The areas of two similar triangles are 36\ c m^2 and 100\ c m^2 . I...

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  20. In given figure, if angleACB=angleCDA,AC=8cm and AD=3 cm, then find BD...

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