Vardaan Learning Institute

Q15. In figure, \(PQ || XY || BC\), \(AP = 2\) cm, \(PX = 1.5\) cm, \(BX = 4\) cm. If \(QY = 0.75\) cm, then \(AQ + CY =\)

• (A) 6 cm
• (B) 4.5 cm
• (C) 3 cm
• (D) 5.25 cm

Q16. Given \(\Delta ABC \sim \Delta PQR\), \(\angle A = 30�\) and \(\angle Q = 90�\). The value of \((\angle R + \angle B)\) is

• (A) \(90�\)
• (B) \(120�\)
• (C) \(150�\)
• (D) \(180�\)

Q23. In figure, \(AP = 1\) cm, \(BP = 2\) cm, \(AQ = 1.5\) cm, \(AC = 4.5\) cm. Prove that \(\Delta APQ \sim \Delta ABC\). Find \(PQ\) if \(BC = 3.6\) cm.

Q32 (a). State and prove the converse of BPT: If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.

Q32 (b). In figure, \(\Delta CAB\) is right-angled at A and \(AD \perp BC\). Prove that \(\Delta ADB \sim \Delta CDA\). If \(BC = 10\) cm and \(CD = 2\) cm, find \(AD\).