It is given that ΔABC ~ ΔXYZ and Area ΔABC : Area ΔXYZ = 81 : 25. If AB = 18 cm, BC = 10 cm, CA = 15 cm, then what is the side XZ (in cm)?
The correct answer is \frac{{25}}{3}.
Ratio of Altitudes/Medians/Angle Bisectors: The ratio of corresponding altitudes, medians, or angle bisectors in similar triangles is also equal to the ratio of their corresponding sides (the scale factor). Conditions for Similarity: Triangles can be proven similar using criteria like AAA (Angle-Angle-Angle), AA (Angle-Angle, since the third angle is determined), SSS (Side-Side-Side - ratios of corresponding sides are equal), and SAS (Side-Angle-Side - two sides are proportional, and the included angle is equal). Understanding these properties is crucial for solving problems involving similar figures in geometry.
Similar Questions
In a triangle, if the angles are in the ratio 1 ∶ 2 ∶ 3, then the ratio of the corresponding sides is:
Given that Δ MAN and Δ CPT are congruent to each other such that ∠M = 75, ∠N = 65, ∠A = 40, ∠C = x/2, ∠P = 6y + 16. Find the value of (x – 5y).
If M is the mid-point of the side BC of ABC, and the area of ABM is 19 cm2 , then the area of ABC is:
It is given that ΔABC ∼ ΔYZX and Ar ΔABC : Ar ΔXYZ = 256 : 25. If AB = 12 cm, BC = 10 cm, CA = 15 cm, then what is the value of YZ (in cm)?
In trapezium ABCD, AB∥DC. The sides AD and BC are produced to meet at E. AB = 15 cm, CD = 10 cm, AD = 4 cm and BC = 5 cm, then DE = ?
In Δ ABC, ∠C = 70°. The bisectors of ∠A and<B meet BC and AC in points D and E, respectively. AD and BE intersect each other at P. What is the measure of ∠DPB?
If angles of triangle are in the ratio 3 : 4 : 5, then find the angles.
In ΔABC, ∠A = 48°. AB and AC is extended to points D and E respectively, if the bisectors of angle CBD and angle BCE meet at point O, then ∠BOC is equal to:
Let ΔABC ~ ΔPQR and \(\frac{{ar\left( {{\rm{\Delta \;ABC}}} \right)}}{{ar\left( {{\rm{\Delta \;PQR}}} \right)}} = \frac{9}{{169}}\) . If AB = 12 cm, BC = 7 cm and AC = 8 cm, then PQ (in cm) is equal to:
The side BC Δ ABC is produced to D. The bisectors of ∠ABC and ∠ACD meet at E. If AB = AC and ∠BEC = 24º, then the measure of ∠ABC is:
Important Questions from Triangles, Congruence and Similarity
If sides of a triangle are 12 cm, 15 cm and 21 cm, then what is the inradius (in cm) of the triangle?
What is the area of quadrilateral ABCD?
Sides of two similar triangles are in the ratio 4 ∶ 9. Area of these triangles are in the ratio:
If the ratio of corresponding sides of 2 similar triangles is 2 ∶ 3. Then the ratio of their corresponding altitude is :
The following theorems present conditions under which triangles are similar. Which is a false condition of the theorem?
