Geometry Similar Right Triangles

Introduction

Similar triangle is one type of triangle in geometry. A 90° angle is called as a right angle. In a right triangle, the total angle value of the remaining angles also equal 90°. In similar right triangles, angle A and angle B together equal 90°. Remember, the total angle value of all three angles is 180°. So angles an A and an angle B must the total angle value up to 90°. In this article we shall discuss about geometry similar right triangles.

 

Geometry Similar right triangles:

 

      The two right triangles are having a same angles value but the length of the sides is not same values, its various from each other. The acute angles of the first triangle are equal to acute angles of the second triangle. This conclusion is supported by the following reasons:

  • The right angle value of the first triangle is equal to the right angle in the second, since all right angle values are equal.
  • The total angle value of the all three angles of any triangle is 180°. Therefore, the total angle value of the two acute angles in a right triangle is 90°.
  • Let the equivalent acute angles in the two triangles be represented by an A and A’ respectively. Then the other acute angles, B and B’, are as follows:
  • B = 90° - A
  • B’ = 90° - A’
  • Since angle an A and angle an A’ are equal in the similarity right triangle, angles B and B’ are also equal in the similarity right triangle.
  • Now we know that two right triangles through one acute angle of the first triangle equal to one acute angle of the second have their complete corresponding angles equal. Thus the two triangles are similar right triangles.
  • If the total angle value of two acute angles of two similarity right triangles are 180° and if two triangles sum of hypotenuse is equal to other two legs is equal then it is said to be similar right triangles.


 

Sample problem for geometry similar right triangles:

 

       The similar right triangles are satisfy the Pythagoras theorem of the area of the square in which side is the side opposite the right angle is equal to the total value of the areas of the squares in which sides are the two legs (the two sides that meet at a right angle).

                      a2 + b2 = c2

 Same like in angles the sum of the two small squares angles equal to the square of big angle.

                      ∠A+∠B=∠C

 

 

Ex 1:  Find c=?  Sides and b are a=4 b=6 side a= 6 and side b=4 c =?

Sol :   For c2 = a2 + b2

                            c2= 42 +62

                            c =`sqrt(16 + 36)`

                            C =`sqrt(54)`

For PQR c2 = a2 + b2

                    c2 = 62+ 42

                    c2 = 54

                    C=`sqrt(54)`

        Therefore the triangles are similar right triangles.