Question

In triangle ABC , let the bisectors of angle b meet AC at D and let the bisect of angle C meet at AB at E. Show that if BD is congruent to CE then angle B is congruent to angle C.

Answer #1

ABC is a right-angled triangle with right angle at A, and AB
> AC. Let D be the midpoint of the side BC, and let L be the
bisector of the right angle at A. Draw a perpendicular line to BC
at D, which meets the line L at point E. Prove that
(a) AD=DE; and
(b) ∠DAE=1/2(∠C−∠B)
Hint: Draw a line from A perpendicular to BC, which meets BC in
the point F

Let J be a point in the interior of triangle ABC. Let D, E, F be
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respectively. If each of the three quadrilaterals AEJF, BFJD, CDJE
has an inscribed circle tangent to all four sides, then J is the
incenter of ∆ABC. It is sufficient to show that J lies on one of
the angle bisectors.

Given ∠B below, construct the triangle △ABC with D on AC so that
BD bisects ∠B and has length bd and satisfies AD/DC=4/5. Show the
steps.

Triangle ABC is a right angle triangle in which
∠B = 90 degree, AB = 5 units , BC = 12 units. CD
and AE are the angle bisectors of ∠C and ∠A
respectively which intersects each other at point I. Find the area
of the triangle DIE.

Consider the triangle ABC. Suppose that the perpendicular
bisectors of line segments AB and BC intersect at point X. Prove
that X is on the perpendicular bisector of line segment AC.

Let 4ABC be an isosceles triangle, where the congruent
sides are
AB and AC. Let M and N denote points on AB and AC
respectively
such that AM ∼= AN. Let H denote the intersection point of MC
with
NB. Prove that the triangle 4MNH is isosceles

Given △ABC, extend sides AB and AC to rays AB and AC forming
exterior angles. Let the line rA be the angle bisector ∠BAC, let
line rB be the angle bisector of the exterior angle at B, and let
line rC be the angle bisector of the exterior angle at C.
• Prove that these three rays are concurrent; that is, that they
intersect at a single point. Call this point EA
• Prove that EA is the center of...

Need to Show that for any triangle, the angle bisectors
intersect. Then, show that the intersection point of the medians,
the intersection point of the altitudes, and the intersection point
of the angle bisectors lie on the same line.

a) In the triangle ABC, angle A is 60 ° and angle B 90 °. The
side AC is 100 cm. How long is the side BC? Determine an exact
value.
b) An equilateral triangle has the height of 11.25 cm. Calculate
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Let A=(0,0), B=(1,1), C=(-1,1), A'(2,0),B'(4,0), C'(2,-2).Show
that triangle ABC and triangle A'B'C' satisfy the hypothesis of
Proposition 2.3.4 in taxicab geometry but are not congruent in
it

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