List of top Mathematics Questions on Triangles asked in CBSE X

A vertical pole of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower.

Sides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and QR and median PM of ∆PQR (see the given figure). Show that ∆ABC ∼ ∆PQR.

Fill in the blanks using the correct word given in the brackets :
(i) All circles are __________. (congruent, similar)
(ii) All squares are __________. (similar, congruent)
(iii) All __________ triangles are similar. (isosceles, equilateral)
(iv) Two polygons of the same number of sides are similar, if (a) their corresponding angles are __________ and (b) their corresponding sides are __________. (equal, proportional)

D is a point on the side BC of a triangle ABC such that \(\angle\)ADC = \(\angle\)BAC. Show that CA²=CB.CD

In the following figure, E is a point on side CB produced of an isosceles triangle ABC with AB = AC. If AD ⊥ BC and EF ⊥ AC, prove that ∆ABD ∼ ∆ECF

CD and GH are respectively the bisectors of ΔACB and ΔEGF, such that D and H lie on sides AB and FE of ΔABC and ΔEFG respectively. If ΔABC ~ ΔFEG, show that:
(i) \(\frac{CD}{GH}=\frac{AC}{FG}\)
(ii) ΔDCB~ΔHGE
(iii) ΔDCA~ΔHGF

In the following figure, ABC and AMP are two right triangles, right-angled at B and M, respectively. Prove that:

(i) ΔABC ~ ΔAMP
(ii) \(\frac{CA}{PA}=\frac{BC}{MP}\)

E is a point on the side AD produced of a parallelogram ABCD and BE intersects CD at F. Show that ΔABE ~ ΔCFB.

In the following figure, altitudes AD and CE of ΔABC intersect each other at the point P.Show that:

(i) ΔAEP ~ ΔCDP
(ii) ΔABD ~ ΔCBE
(iii) ΔAEP ~ Δ ADB
(iv) ΔPDC ~ ΔBEC

Sides AB and AC and median AD of a triangle ABC are respectively proportional to sides PQ and PR and median PM of another triangle PQR. Show that ΔABC∼ΔPQR

If AD and PM are medians of triangles ABC and PQR, respectively where ΔABC ~ ΔPQR, proves that \(\frac{AB}{PQ}=\frac{AD}{PM}\)

S and T are points on sides PR and QR of ΔPQR such that \(\angle\)P = \(\angle\)RTS. Show that ΔRPQ ~ ΔRTS.