SSC (English Medium) 9th Standard - Maharashtra State Board Question Bank Solutions for Geometry

Prove that, if the bisector of ∠BAC of ΔABC is perpendicular to side BC, then ΔABC is an isosceles triangle.

In ΔPQR, If PQ > PR and bisectors of ∠Q and ∠R intersect at S. Show that SQ > SR.

In the figure, point D and E are on side BC of ΔABC, such that BD = CE and AD = AE. Show that ΔABD ≅ ΔACE.

In the given figure, bisector of ∠BAC intersects side BC at point D. Prove that AB > BD.

In the given figure, seg PT is the bisector of ∠QPR. A line through R intersects ray QP at point S. Prove that PS = PR.

In the given figure, seg AD ⊥ seg BC. seg AE is the bisector of ∠CAB and C - E - D. Prove that ∠DAE = `1/2` (∠C - ∠B)

`square`ABCD is a parallelogram, P and Q are midpoints of side AB and DC respectively, then prove `square`APCQ is a parallelogram.

In ΔPQR, PQ = 10 cm, QR = 12 cm, PR = 8 cm. Find out the greatest and the smallest angle of the triangle.

In ΔFAN, ∠F = 80, ∠A = 40°. Find out the greatest and the smallest side of the triangle. State the reason.

In the given figure, in ΔABC, seg AD and seg BE are altitudes, and AE = BD. Prove that seg AD ≅ seg BE.

In the given figure, points X, Y, Z are the midpoints of side AB, side BC and side AC of ΔABC respectively. AB = 5 cm, AC = 9 cm and BC = 11 cm. Find the length of XY, YZ, XZ.

In the given figure, `square`PQRS and `square`MNRL are rectangles. If point M is the midpoint of side PR then prove that,

1. SL = LR
2. LN = `1/2`SQ

In the given figure, ΔABC is an equilateral traingle. Points F, D and E are midpoints of side AB, side BC, side AC respectively. Show that ΔFED is an equilateral traingle.

In the given figure, seg PD is a median of ΔPQR. Point T is the mid point of seg PD. Produced QT intersects PR at M. Show that `"PM"/"PR" = 1/3`.

[Hint: DN || QM]

In the Figure, `square`ABCD is a trapezium. AB || DC. Points P and Q are midpoints of seg AD and seg BC respectively. Then prove that, PQ || AB and PQ = `1/2 ("AB" + "DC")`.

In the adjacent figure, `square`ABCD is a trapezium AB || DC. Points M and N are midpoints of diagonal AC and DB respectively then prove that MN || AB.