Question

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

Answer #1

If ?ABC is an isosceles triangle where AB¯?AC¯, m?A=(2x?20)°,
and m?B=(3x+5)°, then m?C=__________°.

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...

Isosceles triangle base length is 15 inches, it also has 2
congruent sides with 15 inches each. Find the height of the
triangle.

Let ABCD be a rectangle with AB = 4 and BC = 1. Denote by M the
midpoint of line segment AD and by P the leg of the perpendicular
from B onto CM.
a) Find the lengths of P B and PM.
b) Find the area of ABPM.
c) Consider now ABCD being a parallelogram. Denote by M the
midpoint of side AD and by P the leg of the perpendicular from B
onto CM. Prove that AP =...

In an isosceles triangle ABC ,AB=BC,angle B=20 . M and N are on
AB and BC respectively such that angle MCA =60, angle NAC =50.find
angle MNC

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.

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

5. Suppose that the incenter I of ABC is on the triangle’s Euler
line. Show that the triangle is isosceles.
6. Suppose that three circles of equal radius pass through a
common point P, and denote by A, B, and C the three other points
where some two of these circles cross. Show that the unique circle
passing through A, B, and C has the same radius as the original
three circles.
7. Suppose A, B, and C are distinct...

prove that if C is an element of ray AB and C is not equal to A,
then ray AB = ray AC using any of the following corollarys
3.2.18.) Let, A, B, and C be three points such that B lies on
ray AC. Then A * B * C if and only if AB < AC.
3.2.19.) If A, B, and C are three distinct collinear points,
then exactly one of them lies between the other two.
3.2.20.)...

Consider a cicle with AB as diameter and P another point on the
circle. Let M be the foot of the perpendicular from P to AB. Draw
the circles which have AM and M B respectively as diameters, which
meet AP at Q are BP are R. Prove that QR is tangent to both
circles.
Hint: As well as the line QR, draw in the line segments M Q and
M R.

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