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

Diagonals of a square IJKL intersects at point M, Find the measures of ∠IMJ, ∠JIK and ∠LJK .

State with reason whether the following statement is ‘true’ or ‘false’.

Every square is a rectangle.

State with reason whether the following statement is ‘true’ or ‘false’.

Every square is a rhombus.

If the diagonal of a square is `12 sqrt 2` cm then the perimeter of square is ______.

If diagonal of a square is 13 cm then find its side.

What is the form of co-ordinates of a point on the X-axis?

Any point on the line y = x is of the form ______.

In which quadrant does the point (-4, -3) lie?

What is the nature of the line which includes the points (-5, 5), (6, 5), (-3, 5), (0, 5)?

Which of the points P(-1, 1), Q(3, - 4), R(1, -1), S (-2, -3), T(-4, 4) lie in the fourth quadrant?

Which of the following statements is true?

In the following example, a pair of triangles is shown. Equal parts of triangles in each pair are marked with the same sign. Observe the figure and state the test by which the triangle in each pair are congruent.

By ______ test

Δ ABC  ≅  ΔPQR

In the following example, a pair of triangles is shown. Equal parts of triangle in each pair are marked with the same sign. Observe the figure and state the test by which the triangle in each pair are congruent.

 By ______ test

ΔXYZ ≅ ΔLMN

In the following example, a pair of triangles is shown. Equal parts of triangle in each pair are marked with the same sign. Observe the figure and state the test by which the triangles in each pair are congruent.

 By ______ test

ΔPRQ ≅ ΔSTU

In the following example, a pair of triangles is shown. Equal parts of triangle in each pair are marked with the same sign. Observe the figure and state the test by which the triangle in each pair are congruent.

By ______ test

ΔLMN ≅ ΔPTR

Observe the information shown in pair of triangle given below. State the test by which the two triangles are congruent. Write the remaining congruent parts of the triangles.

From the information shown in the figure,

In ΔABC and ΔPQR

∠ABC ≅ ∠PQR

seg BC ≅ seg QR

∠ACB ≅ ∠PRQ

∴ ΔABC ≅ ΔPQR         ...`square` test

∴ ∠BAC ≅ `square`               ...corresponding angles of congruent triangles.

`{:("seg AB" ≅ square),("and"  square ≅ "seg PR"):}}`      ...corresponding sides of congruent triangles

What will be the volume of a cube having length of edge 7.5 cm?

Observe the information shown in pair of triangle given below. State the test by which the two triangles are congruent. Write the remaining congruent parts of the triangles.

From the information shown in the figure,

in ΔPTQ and ΔSTR

seg PT ≅ seg ST

∠PTQ ≅ ∠STR        ...[Vertically opposite angles]

∴ ΔPTQ ≅ ΔSTR       ...`square` test

∴ `{:("∠TPQ" ≅ square),("and"  square ≅ "∠TRS"):}}`      ...corresponding angles of congruent triangles

seg PQ ≅ `square`         ...corresponding sides of congruent triangles

From the information shown in the figure, state the test assuring the congruence of ΔABC and ΔPQR. Write the remaining congruent parts of the triangles.

As shown in the following figure, in ΔLMN and ΔPNM, LM = PN, LN = PM. Write the test which assures the congruence of the two triangles. Write their remaining congruent parts.