In a ∆ABC, if AB=AC and ∠A=70°, find ∠B and ∠C.

The vertical angle of an isosceles triangle is 100°. Find its base angles.

In a ∆ABC, if AB=AC and ∠B=65°, find ∠C and ∠A.

In an isosceles triangle, if the vertex angle is twice the sum of the base angles, calculate the angles of the triangle.

What is the measure of each of the equal angles of a right-angled isosceles triangle?

If the base of an isosceles triangle is produced on both sides, prove that the exterior angles so formed are equal to each other.

Find the measure of each exterior angle of an equilateral triangle.

In the given figure, O is the midpoint of each of the line segments AB and CD. Prove that AC=BD and AC||BD.

In the adjoining figure, PA ⊥ AB, QB ⊥ AB and PA=QB. If PQ intersects AB at O, show that O is the midpoint of AB as well as that of PQ.

Let the line segments AB and CD intersect at O in such a way that OA=OD and OB=OC. Prove that AC=BD but AC may not be parallel to BD.

In the given figure, ﺎ‖m and M is the midpoint of AB. Prove that M is also the midpoint of any line segment CD having its end points atﺎ and m respectively.

In the given figure, AB=AC and OB=OC. Prove that ∠ABO=∠ACO. Give that AB=AC and OB=OC.

In the given figure, ABC is a triangle in which AB=AC and D is a point on AB. Through D, a line DE is drawn parallel to BC and meeting AC at E. Prove that AD=AE.

In the adjoining figure, X and Y are respectively two points on equal sides AB and AC of ∆ABC such that AX=AY. Prove that CX=BY.

In the given figure, C is the midpoint of AB. If ∠DCA=∠ECB and ∠DBC=∠EAC, prove that DC=EC.

In the given figure, BA ⊥ AC and DE ⊥ EF such that BA=DE and BF=DC. Prove that AC=EF.

In the given figure, if x=y and AB=CB, then prove that AE=CD.

ABC is a triangle in which AB=AC. If the bisectors of ∠B and ∠C meet AC and AB in D and E respectively, prove that BD=CE.

In the adjoining figure, AD is a median of ∆ABC. If BL and CM are drawn perpendiculars on AD and AD produced, prove that BL=CM

In ∆ABC, D is the midpoint of BC. If DL ⊥ AB and DM ⊥ AC such that DL=DM, prove that AB=AC.

In ∆ABC, AB=AC and the bisectors of ∠B and ∠C meet at a point O. prove that BO=CO and the ray AO is the bisector of ∠A.

In the given figure, PQR is an equilateral triangle and QRST is a square. Prove that

(i) PT=PS, (ii) ∠PSR=15°.

In the given figure, ABC is a triangle, right angled at B. If BCDE is a square on side BC and ACFG is a square on AC, prove that AD=BF.

Prove that median from the vertex of an isosceles triangle is the bisector of the vertical angle.

In the given figure, ABCD is a quadrilateral in which AB‖DC and P is the midpoint of BC. On producing, AP and DC meet at Q. prove that (i) AB=CQ, (ii) DQ=DC+AB.

In the given figure, OA=OB and OP=OQ. Prove that (i) PX=QX, (ii) AX=BX.

In the given figure, ABCD is a square and P is a point inside it such that PB=PD. Prove that CPA is a straight line.

In the given figure, ABC is an equilateral triangle, PQ ‖AC and AC is produced to R such that CR=BP. Prove that QR bisects PC.

In the given figure, ABCD is a quadrilateral in which AB=AD and BC=DC. Prove that (i) AC bisects ∠A and ∠C, (ii) AC is the perpendicular bisector of BD.

In the given figure, the bisectors of ∠B and ∠C of ∆ABC meet at I If IP ⊥BC, IQ ⊥CA and IR ⊥ AB, prove that

(i) IP=IQ=IR, (ii) IA bisects ∠A.

In the adjoining figure, P is a point in the interior of ∠AOB. If PL ⊥ OA and PM ⊥ OB such that PL=PM, show that OP is the bisector of ∠AOB

In the given figure, ABCD is a square, M is the midpoint of AB and PQ ⊥ CM meets AD at P and CB produced at Q. prove that (i) PA=BQ, (ii) CP=AB+PA.

In the adjoining figure, explain how one can find the breadth of the river without crossing it.

In ∆ABC, if ∠A=36° and ∠B=64°, name the longest and shortest sides of the triangle.

In ∆ABC, if ∠A=90°, which is the longest side?

In ∆ABC, if ∠A=∠B=45°, name the longest side.

In ∆ABC, side AB is produced to D such that BD=BC. If ∠B=60° and ∠A=70°, prove that (i) AD>CD and (ii) AD>AC.

In ∆ABC, ∠B=35°,∠C=65° and the bisector of ∠BAC meets BC in X. Arrange AX, BX and CX in descending order.

In ∆ABC, if AD is the bisector of ∠A, show that AB>BD and AC>DC

In the given figure, ABC is a triangle in which AB=AC. If D be a point on BC produced, prove that AD>AC.

In the adjoining figure, AC>AB and AD is the bisector of ∠A. show that ∠ADC>∠ADB.

In ∆PQR, if S is any point on the side QR, show that PQ+QR+RP>2PS.

In the given figure, O is the center of the circle and XOY is a diameter. If XZ is any other chord of the circle, show that XY>XZ.

If O is a point within ∆ABC, show that:

(i) AB+AC>OB+OC

(ii) AB+BC+CA>OA+OB+OC

(iii) OA+OB+OC>(AB+BC+CA)

Can we draw a triangle ABC with AB=3cm, BC=3.5cm and CA=6.5cm? Why?

Which of the following is not a criterion for congruence of triangles?

If AB=QR, BC=RP and CA=PQ, then which of the following holds?

If ∆ABC≅∆PQR AND ∆ABC is not congruent to ∆RPQ, then which of the following is not true?

It is given that ∆ABC≅∆FDE in which AB=5cm, ∠B=40°, ∠A=80° and FD=5cm. Then, which of the following is true?

In ∆ABC, AB=2.5cm and BC=6cm. Then, the length of AC cannot be

In ∆ABC, ∠A=40° and ∠B=60°, Then, the longest side of ∆ABC is

In ∆ABC, ∠B=35°, ∠C=65° and the bisector AD of ∠BAC meets BC at D. Then, which of the following is true?

In the given figure, AB>AC. Then, which of the following is true?

In the given figure, AB>AC. If BO and CO are the bisectors of ∠B and ∠C respectively, then

In the given figure, AB=AC and OB=OC. Then, ∠ABO: ∠ACO=?

In ∆ABC, IF ∠C>∠B, then

O is any point in the interior of ∆ABC. Then, which of the following is true?

If the altitudes from two vertices of a triangle to the opposite sides are equal, then the triangle is

In the given figure, AE=DB, CB=EF And ∠ABC=∠FED. Then, which of the following is true?

In the given figure, BE ⊥ CA and CF ⊥ BA such that BE=CF. Then, which of the following is true?

In the given figure, D is the midpoint of BC, DE ⊥ AB and DF ⊥ AC such that DE=DF. Then, which of the following is true?

In ∆ABC and ∆DEF, it is given that AB=DE and BC=EF. In order that ∆ABC≅∆DEF, we must have

In ∆ABC and ∆DEF, it is given that ∠B=∠E and ∠C=∠F. In order that ∆ABC ≅ DEF, we must have

In ∆ABC and ∆PQR, it is given that AB=AC, ∠C=∠P and ∠P=∠Q. Then, the two triangles are

Which is true?

Three statements are given below:

(I) In a ∆ABC in which AB=AC, the altitude AD bisects BC.

(II) If the altitudes AD, BE and CF of ∆ABC are equal, then ∆ABC is equilateral.

(III) If D is the midpoint of the hypotenuse AC of a right ∆ABC, then BD=AC.

Which is true?

The question consists of two statements, namely, Assertion (A) and Reason (R). Please select the correct answer.

The question consists of two statements, namely, Assertion (A) and Reason (R). Please select the correct answer.

The question consists of two statements, namely, Assertion (A) and Reason (R). Please select the correct answer.

The question consists of two statements, namely, Assertion (A) and Reason (R). Please select the correct answer.

The question consists of two statements, namely, Assertion (A) and Reason (R). Please select the correct answer.

Match the following columns.

The correct answer is:

(A)-………, (B)-………, (C)-…….., (D)-……..,

Fill in the blanks with < or >.

(A) (Sum of any two sides of a triangle)………… (the third side)

(B) (Difference of any two sides of a triangle)………… (the third side)

(C) (Sum of three altitudes of a triangle)………… (sum of its three sides)

(D) (Sum of any two sides of a triangle)…….. (twice the median to the 3^rd side)

(E) (Perimeter of a triangle)…………. (Sum of its three medians)

Fill in the blanks:

(A)Each angle of an equilateral triangle measures……………..

(B) Medians of an equilateral triangle are…………

(C) In a right triangle the hypotenuse is the ……….side.

(D) Drawing a ∆ABC with AB=3cm, BC=4cm and CA=7cm is………..

In an equilateral ∆ABC, find ∠A.

In a ∆ABC, if AB=AC and ∠B=65°, find ∠A.

In a right ∆ABC, ∠B=90°. Find the longest side.

In a ∆ABC, ∠B > ∠C. Which of AC and AB is longer?

Can we construct a ∆ABC in which AB=5cm, BC=4cm and AC=9cm? Why?

Find the measure of each exterior angle of an equilateral triangle.

Show that the difference of any two sides of a triangle is less than the third side

In a right ∆ABC, ∠B=90° and D is the mid-point of AC. Prove that BD=AC.

Prove that the perimeter of a triangle is greater than the sum of its three medians

Which is true?

(A) A triangle can have two acute angles.

(B) A triangle can have two right angles.

(C) A triangle can have two obtuse angles.

(D) An exterior angles of a triangle is always less than either of the interior opposite angles.

In ∆ABC, BD ⊥ AC and CE ⊥ AB such that BE=CD. Prove that BD=CE.

In ∆ABC, AB=AC. Side BA is produced to D such that AD=AB.

Prove that ∠BCD=90°.

In the given figure, it is given that AD=BC and AC=BD.

Prove that ∠CAD=∠CBD and ∠ADC=∠BCD.

Prove that the angles opposite to equal sides of a triangle are equal

In an isosceles ∆ABC, AB=AC and the bisectors of ∠B and ∠C intersect each other at O. Also, O and A are joined.

Prove that: (i) OB=OC (ii) ∠OAB=∠OAC

Prove that, of all line segments that can be drawn to a given line, from a point, not lying on it, the perpendicular line segment is the shortest

Each question consists of two statements, namely, Assertion (A) and Reason (R). Please select the correct answer.

Each question consists of two statements, namely, Assertion (A) and Reason (R). Please select the correct answer.

Math the following columns:

The correct answer is:

(a)-……, (b)-……, (c)-……., (d)-……

In the given figure, PQ>PR and QS and RS are the bisectors of ∠Q and ∠R respectively. Show that SQ>SR

In the given figure, ABC is a triangle right-angled at B such that ∠BCA=2∠BAC.

Show that AC=2BC.

S is any point in the interior of ∆PQR.

Show that (SQ+SR)<(PQ+PR).

Show that in a quadrilateral ABCD

AB+BC+CD+DA>AC+BD.