# HYPOTENUSE LEG THEOREM

## About "Hypotenuse Leg Theorem"

Hypotenuse Leg Theorem :

Hypotenuse leg theorem is the theorem which can be used to prove the congruence of two right triangles.

## Hypotenuse Leg Theorem

Explanation :

If the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, then the two right triangles are congruent.

This principle is known as Hypotenuse-Leg theorem.

## Hypotenuse Leg Theorem - Examples

Example 1 :

Check whether two triangles ABD and ACD are congruent.

Solution :

(i) Triangle ABD and triangle ACD are right triangles. Because they both have a right angle.

(i) AB  =  AC (Hypotenuse)

(ii) AD  =  AD (Common side, Leg)

Hence, the two triangles ABD and ACD are congruent by Hypotenuse-Leg (HL) theorem.

Example 2 :

Check whether two triangles PQR and WXY are congruent.

Solution :

(i) Triangle PQR and triangle WXY are right triangles. Because they both have a right angle.

(i) PQ  =  XY (Hypotenuse).

(ii) PR  =  WX (Leg)

Hence, the two triangles PQR and WXY are congruent by Hypotenuse-Leg theorem.

## Other Triangle Congruence Postulates and Theorems

1. Side-Side-Side (SSS) Congruence Postulate

If three sides of one triangle is congruent to three sides of another triangle, then the two triangles are congruent.

2. Side-Angle-Side (SAS) Congruence Postulate

If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent.

3. Angle-Side-Angle (ASA) Congruence Postulate

If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the two triangles are congruent.

4. Angle-Angle-Side (AAS) Congruence Postulate

If two angles and non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle, then the two triangles are congruent.

5. Leg-Acute (LA) Angle Theorem

If a leg and an acute angle of one right triangle are congruent to the corresponding parts of another right triangle, then the two right triangles are congruent.

6. Hypotenuse-Acute (HA) Angle Theorem

If the hypotenuse and an acute angle of a right triangle are congruent to the hypotenuse and an acute angle of another right triangle, then the two triangles are congruent.

7. Leg-Leg (LL) Theorem

If the legs of one right triangle are congruent to the legs of another right triangle, then the two right triangles are congruent.

Apart from the problems given above, if you need more problems on triangle congruence postulates,

After having gone through the stuff given above, we hope that the students would have understood, "Hypotenuse Leg Theorem".

Apart from the stuff given in this section if you need any other stuff in math, please use our google custom search here.

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations

Word problems on linear equations

Word problems on quadratic equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6