# Bisector 2

ABC is an isosceles triangle. While AB=AC, AX is the bisector of the angle ∢BAC meeting side BC at X. Prove that X is the midpoint of BC.

### Correct answer:

Tips for related online calculators

Calculation of an isosceles triangle.

See also our right triangle calculator.

See also our trigonometric triangle calculator.

See also our right triangle calculator.

See also our trigonometric triangle calculator.

#### You need to know the following knowledge to solve this word math problem:

#### Units of physical quantities:

#### Themes, topics:

#### Grade of the word problem:

We encourage you to watch this tutorial video on this math problem: video1

## Related math problems and questions:

- Triangle ABC

In a triangle ABC with the side BC of length 2 cm. Point K is the middle point of AB. Points L and M split the AC side into three equal lines. KLM is an isosceles triangle with a right angle at point K. Determine the lengths of the sides AB, AC triangle A - Draw triangle

Construct an isosceles triangle ABC, if AB = 7cm, the size of the angle ABC is 47°, arms | AC | = | BC |. Measure the size of the BC side in mm. - Isosceles 71154

Calculate all interior angles in the isosceles triangle ABC if we know that BC is the base, and we also know: | ∢BAC | = α; | CABCA | = 4α - Bisectors

As shown, in △ ABC, ∠C = 90°, AD bisects ∠BAC, DE⊥AB to E, BE = 2, BC = 6. Find the perimeter of triangle △ BDE. - As shown

As shown, in △ ABC, ∠C = 90°, AD bisects ∠BAC, DE⊥AB to E, BE = 2, BC = 6, then the perimeter of △ BDE - Calculate 60993

In the right triangle ABC, calculate the magnitude of the interior angles if / AB / = 13 cm; / BC / = 12 cm and / AC / = 5 cm. - The right triangle

In the right triangle ABC with a right angle at C, we know the side lengths AC = 9 cm and BC = 7 cm. Calculate the length of the remaining side of the triangle and the size of all angles. - Isosceles - isosceles

It is given a triangle ABC with sides /AB/ = 3 cm /BC/ = 10 cm, and the angle ABC = 120°. Draw all points X such that the BCX triangle is an isosceles and triangle ABX is an isosceles with the base AB. - Similarity of triangles

If triangle ABC ~ to triangle XYZ, AC = 24, AB = 15, BC = 17, and XY = 9, what is the perimeter of triangle XYZ? Round all sides to 1 decimal place. - Sin cos tan

In triangle ABC, right-angled at B. Sides/AB/=7cm, /BC/=5cm, /AC/=8.6cm. Find two decimal places. A. Sine C B. Cosine C C. Tangent C. - Triangle KLB

It is given equilateral triangle ABC. From point L, the midpoint of the side BC of the triangle, it is drawn perpendicular to the side AB. The intersection of the perpendicular and the side AB is point K. How many percents of the area of the triangle ABC - Katy MO

Kate drew a triangle ABC. The middle of the line segment AB has marked as X and the center of the side AC as Y. On the side BC, she wants to find point Z so that the area of a 4gon AXZY is the greatest. What part of the ABC triangle can maximally occupy 4 - Equilateral 4301

Triangle ABC is equilateral with a side length of 8 cm. Points D, E, and F are the sides AB, BC, and AC midpoints. Calculate the area of triangle DEF. In what ratio is the area of triangle ABC to the area of triangle DEF? - Coordinates 32183

The triangle ABC is given in the plane. A (-3,5), B (2,3), C (-1, -2) write the coordinates of the vectors u, v, w if u = AB, v = AC, and w = BC. Enter the coordinates of the centers of the lines SAB (..), SAC (...), SBC (. ..) - Isosceles 2588

Given an isosceles trapezoid ABCD, in which | AB | = 2 | BC | = 2 | CD | = 2 | DA | holds. On its side BC, the point K is such that | BK | = 2 | KC |, on its CD side, the point L is such that | CL | = 2 | LD |, and on its DA side, the point M is such that - (instructions: 3314

Find the distance of the parallels, which equations are: x = 3-4t, y = 2 + t and x = -4t, y = 1 + t (instructions: select a point on one line and find its distance from the other line) - An angle

An angle x is opposite side AB which is 10, and side AC is 15, which is the hypotenuse side in triangle ABC. Calculate angle x.