Exercise 6.5: Pythagoras Theorem

In ΔABC, D and E are points on sides AB and AC respectively. If AD = 3 cm, DB = 4 cm, AE = 4.5 cm, and EC = 6 cm, which of the following is true about DE and BC?

In a right-angled triangle PQR, right-angled at Q, if PQ = 5 cm and QR = 12 cm, what is the length of PR?

Consider two triangles, ΔABC and ΔDEF. If ∠A = 50°, ∠B = 60°, ∠D = 50°, and ∠F = 70°, which similarity criterion would prove ΔABC ~ ΔDEF?

In triangle PQR, points S and T are on PQ and PR respectively. If PS = 3 cm, SQ = 6 cm, PT = 4 cm, and TR = 8 cm, which of the following statements is true?

For two triangles ΔLMN and ΔRST to be similar by the SAS (Side-Angle-Side) criterion, which of the following sets of conditions is sufficient?

Consider two triangles, ΔABC and ΔXYZ. If AB/XY = BC/YZ = CA/ZX, which similarity criterion applies?

Consider two triangles, ΔABC and ΔDEF. Which of the following statements is **incorrect**?

Consider a quadrilateral ABCD. E and F are points on AD and BC respectively such that EF is parallel to AB. If AE/ED = BF/FC, which of the following statements must be true?

A ladder 10 m long reaches a window 8 m above the ground. The distance of the foot of the ladder from the base of the wall is 6 m. Which of the following statements is true about the wall and the ground?

In ΔABC, D and E are points on AB and AC respectively such that DE || BC. If Area(ΔADE) : Area(ΔABC) = 4 : 9, and AD = (x + 3) cm, DB = (x - 2) cm, find the value of x.