Lesson 37 Area of a Triangle Rectangular Area – Part 2

							      Lesson 62
Classifying Triangles
Acute angle
                    Right angle




              Obtuse angle
Acute Triangle

                           Obtuse triangle




          Right triangle
When describing triangles we may refer to the sides and
angles as “opposite” each other. For example, we might
say, “The side opposite the right angle is the longest side
of a right triangle.” The side opposite an angle is the
side “on the other side of” the triangle.



              B             In this right triangle, AB
                            is the side opposite     C,
                            and angle C is the angle
                            opposite side AB.


A            C
Name the sides of this triangle in order from shortest to
longest.

                               W




                        61 °       60 °
                 Y                          X
The sum of the measures of all 3 angles is 180°, so the measure
                     of angle W is 59°.
  Since angle W is the smallest of the three angles, the side
     opposite angle W, which is XY, is the shortest side.


                                W
 The next angle in                         The largest angle is
order of size is angle                     angle Y, so WX is
X, so YW is the next                        the longest side.
     longer side.



                         61 °       60 °
                  Y                        X
Which sides of this triangle are the same length?


                                               If two angles of a
                                Q            triangle are the same
                                              measure, then their
                                             opposite sides are the
                                                  same length.




                         58 °       61 °
                  S                         R
 First we find that the measure of angle Q is 61°. So angles Q
and R have the same measure. This means that their opposite
 sides are the same length. The side opposite angle Q is SR.
The side opposite angle R is SQ. So the sides that are the same
                     length are SR and SQ.

                             Q




                      58 °       61°
                S                         R
In ∆ JKL, JK = KL = LJ. Find the measure of angle J.



                        J
                                    If all three angles of a
                                    triangle are the same
                                       measure, then all
                                      three sides are the
                                          same length.




            L                       K
If two or more sides of a triangle are the same length, then the
angles opposite those sides are equal in measure. In ∆ JKL, all
three sides are the same length, so all three angles are the same
measure. The angles equally share 180°. We find the measure
              of each angle by dividing 180° by 3.

                             J
                                               180° ÷ 3 = 60°

                                             We find that the
                                            measure of angle J is
                                                   60°.



                L                          K
 The triangle in Example 3 is a regular triangle, also called an
equilateral triangle. The three angles of an equilateral triangle
  each measure 60°, and the three sides are the same length.



                   J




    L                           K
 If a triangle has at least two sides of the same length (and
thus two angles of the same measure), the triangle is called
    an isosceles triangle. The triangle in Example 2 is an
        isosceles triangle as are each of these triangles.




                     45 °         45 °
       40 °


70 °          70 °
                                                100 °
                                         40 °           40 °
     If the three sides of a triangle are all different lengths and the
     angles are all different measures, then the triangle is called a
    scalene triangle. Here we show a scalene triangle, an isosceles
                   triangle and an equilateral triangle.




                           Scalene triangles have
                           three sides that are all
                             different lengths.
Isosceles triangles have                              Equilateral triangles
 at least two sides that                              have three sides that
  are the same length.                                are the same length.
                                                      Equilateral triangles
                                                      are regular triangles.
The perimeter of an equilateral triangle is 2 feet. How many
inches long is each side?


                              A




                 C                        B
  All three sides of an equilateral triangle are equal in length.
Since 2 feet equals 24 inches, we divide 24 inches by 3 and find
             that the length of each side is 8 inches.
               A


                                       24 inches ÷ 3 = 8 inches




 C                            B
Sketch an isosceles right triangle.
We sketch a right angle, making both segments equal in
length.
Then, we complete the triangle.



                     For more triangle fun…
Are you a triangle
expert????


      Let’s find out…
                        Puppies.
All 3 angles of the triangle
 measures less than 90°.
A triangle that contains one angle
       that measures 90°.
A triangle that contains one angle
  that measures more than 90°.
☺