\begin{aligned} &\text { In the figure alongside, }\\ &A; B=A C\\ &\angle \mathrm{A}=48^{\circ} \text { and }\\ &\angle \mathrm{ACP}=18^{\circ} \end{aligned}
Show that: BC=CD.
Calculate:
In the given figure, AB=AC. Prove that:
(i) DP=DQ
(ii) AP=AQ
(iii) AD bisects angle A
In the following figure, AB=AC; BC=CD and DE is parallel to BC. Calculate:
Calculate x:
In the figure, given below, AB=AC.
In the figure given below, LM=LN; angle PLN=1100. Calculate:
An isosceles triangle ABC has AC=BC. CD bisects AB at D and CAB=550.
Find:
(i)<\mathrm{DCB}
\text { (ii) } \angle \mathrm{CBD}
Find x:
In the triangle ABC, BD bisects angle B and is perpendicular to AC. If the lengths
of the sides of the triangle are expressed in terms of x and y as shown, find the
values of x and y.
\text { In the given figure; AE\|BD, AC IIED and AB=AC. Find } \angle \mathrm{a}, \angle \mathrm{b} \text { and } \angle \mathrm{c} \text { . }
\text { In the figure of Q.no.11, given above, if } \mathrm{AC}=\mathrm{AD}=\mathrm{CD}=\mathrm{BD} ; \text { find } \angle \mathrm{ABC} \text { . }
In the following figure, BL=CM.
\begin{aligned} &\text { In triangle } \mathrm{ABC} ; \angle \mathrm{ABC}=90^{\circ}, \text { and } \mathrm{P} \text { is a point on } \mathrm{AC} \text { such that } \angle \mathrm{PBC}=\angle \mathrm{PCB} \text { . }\\ &\text { Show that } P A=P B \text { . } \end{aligned}
ABC is an equilateral triangle. Its side BC is produced up to point E such that C is
the midpoint of BE. Calculate the measure of angles ACE and AEC.
\text { In triangle } A B C, D \text { is a point in } A B \text { such that } A C=C D=D B \text { . If } \angle B=28^{0}, \text { find the angle }ACD.
Prove that a triangle ABC is isosceles, if:
\text { (i) Altitude AD bisects } \angle \mathrm{BAC} \text { , or }
\text { (ii) Bisector of } \angle \mathrm{BAC} \text { is perpendicular to base BC. }
In the given figure;
AB=BC and AD=EC.
Prove that: BD=BE.
If the equal sides of an isosceles triangle are produced, prove that the exterior
angles so formed are obtuse and equal.
In triangle ABC, AB=AC; BE⊥ AC and CF⊥AB. Prove that:
(i) BE=CF
(ii) AF=AE
An isosceles triangle ABC, AB=AC. The side BA is produced to D such that
BA=AD. Prove that: \angle B C D=90^{\circ}
(i) In a triangle ABC, AB=AC, and ∠A=360. If the internal bisector of ∠C meets
AB at point D, proves that AD=BC.
(ii) If the bisector of an angle of a triangle bisects the opposite side, prove that
the triangle is isosceles.
Prove that the bisectors of the base angles of an isosceles triangle are equal.
The bisectors of the equal angles B and C of an isosceles triangle ABC meet at O.
Prove that AO bisects angle A.
ABC and DBC are two isosceles triangle on the same side of BC. Prove that:
(i) DA (or AD) produced bisects BC at the right angle
(ii) ∠BDA=∠CDA
Prove that the medians corresponding to equal sides of an isosceles triangle are
equal.
Use the given figure to prove that, AB=AC.
In the given figure; AE bisects exterior angle CAD and AE is parallel to BC.
Prove that: AB=AC.
In an equilateral triangle ABC; points P, Q and R are taken on the sides AB, BC, and CA respectively such that AP= BQ= CR. Prove that triangle PQR is
equilateral.
In triangle ABC, altitudes BE and CF is equal. Prove that the triangle is
isosceles.
Through any point in the bisector of an angle, a straight line is drawn parallel to
either arm of the angle. Prove that the triangle so formed is isosceles.
In triangle ABC; AB=AC. P, Q, and R are mid-points of sides AB, AC, and BC
respectively. Prove that:
(i) PR= QR
(ii) BQ = CP
Equal sides AB and AC of an isosceles triangle ABC are produced. The bisectors
of the exterior angles so formed meet at D. Prove that AD bisects angle A.
ABC is a triangle. The bisector of the angle BCA meets AB in X. A point Y lies on
CX such that AX=AY.
\text { Prove that: } \angle \mathrm{CAY}=\angle \mathrm{ABC}
In the following figures; IA and IB are bisectors of angles CAB and CBA
respectively. CP is parallel to IA and CQ is parallel to IB.
Prove that:
PQ= The perimeter of the triangle ABC.
Sides AB and AC of a triangle ABC are equal. BC is produced through C up to
point D such that AC=CD. D and A are joined and produced (through vertex A)
up to point E. If angle BAE=1080; find angle ADB.
The given figure shows an equilateral triangle ABC with each side 15 cm. Also
DE||BC, DF||AC and EG||AB.
If all the three altitudes of a triangle are equal, the triangles are equilateral. Prove
it.
In a triangle, ABC, the internal bisector of angle A meets the opposite side BC at point
D. Through vertex C, line CE is drawn parallel to DA which meets BA produced at
point E. Show that triangle ACE is isosceles.
In triangle ABC, the bisector of angle BAC meets the opposite side BC at point D. If BD =
CD, prove that triangle ABC is isosceles.
In triangle ABC, D is a point on BC such that AB = AD = BD= DC. Show that:
\angle \mathrm{ADC}: \angle \mathrm{C}=4: 1
Using the information given in each of the following figures, find the value of a
and b.
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