The lengths of the 2 legs of right triangle △ABC shown below are given in inches 24, 32 respec. The midpoint of AB is how many inches from A ?

Given BD bisects ∠ABC , ∠A+∠C=180° . Prove AD=DC

Given quadrilateral ABCD , BC > BA , AD = DC , BD bisects ∠BAC . Prove ∠BAD + ∠C = 180°

In the triangle △ ABC , AB=AC , E is a point on AB , F is on extension line of AC , BE=CF , prove DE=DF 。

In △ABC , D is the midpoint of BC , EF crossing D intersects AB at point E and AE at F , and BE = CF , prove AE = AF

The obtuse Isosceles triangle ABC has two sides with length a and one side length b . The length of side a= 8 . The length of side b=3a . Find the perimeter of △ABC .

Given the right triangle paper sheet ABC , AC = 15cm, ∠B = 90°

(1) If AB=8.5cm , fold the triangle ABC to make point B fall on the side of AC as point E , the line made by folding is AD 。Find the length of EC .

(2) Assuming AB = x , first fold the triangle as (1) ,and then fold the triangle ADE along the line DE to make point A fall on the ray of EC as point F . In the folded shape, if the segment CF= \dfrac{1}{2}EF , what is the value of x ?

In the equilateral triangles ABC and BCD, the length of side is 1. What is the distance from A to D?

The equilateral triangle ABC has an area of 900m^2 . Points D and E are the mid points of the side AB and AC respectively. Find the area of the △DEF .

Proofs of The Pythagorean Theorem

Determine the area of the triangle enclosed by the lines y = - 4 , x = 1 and y = -2x + 8 .

In △ABC , medians BE and CD are perpendicular to each other and intersect at Z . If BE = 8 cm, CD = 12 cm, what is the area of △ABC ?