The document defines and describes different types of triangles: equilateral, isosceles, right, scalene, acute-angled, and obtuse-angled. It provides examples of each type of triangle through diagrams. It also discusses properties of triangles, such as interior angles always summing to 180 degrees and the sum of two opposite angles equaling the outside angle.

1. BY: KAREEMA DOMINGO
STUDENT NUMBER: 200971653

2. WHAT IS A TRIANGLE?
Triangles are shapes with three straight sides.

3. * An EQUILATERAL TRIANGLE is a triangle
with all three sides of equal length. The
three angles are also all equal.
* An ISOSCELES TRIANGLE is a triangle
with two sides of equal length. The two
angles opposite the equal sides are also
equal to one another.
* A RIGHT-ANGLED TRIANGLE is a triangle
with one angle that is a right angle.

4. * A SCALENE TRIANGLE is a triangle with all
the sides of different lengths. The angles
are also all different.
* An ACUTE-ANGLED triangle is a triangle with
all the sides acute, i.e. less than 90°.
* An OBTUSE-ANGLED triangle is a triangle
with one obtuse angle, i.e. more than 90°.

5. It is a general convention that equal
sides are marked by drawing a short
line, /, through them , and a right
angle is marked by a square between
the arms of the angle . If sides
and angles are not marked, do not
assume that they are equal, just
because they look equal!

6. The interior angles of a triangle always add up
to 180°. Because of this, only one of the angles
can be 90° or more. In a right triangle, since
one angle is always 90°, the other two must
always add up to 90°.(i.e. V1 + V2 + V3 = 180°)
The sum of the two opposite angles in a triangle is
50° equal to the outside angle. Therefore, angles
a
a + b = d and, angle b = d (110°) – a (50°) = 60°.
As a result, c = 80°. Reason, the interior angles of a
triangle always adds up to 180°.
b c 110° d

7. a. What kind of triangle is shown in
each of the diagrams ?
Pare the options below with the
letter of the triangle:
b.
Acute
Obtuse
c. Right triangle
Scalene
Isosceles
d. Equilateral

8. The "Many Triangles" problem
In the figure below, the lines BC, AD and FT are parallel.

9. Problem 1
How many right triangles are there?
(If you are assuming the angle abk, and the three
others like it, is 90° you will need to prove it first).
Problem 2
How many isosceles triangles are there?
Problem 3
How many triangles altogether?

10. A. In the shape abcd, the angles
d
b = 30°and c = 75°. Calculate
a angles a and d. Give reasons
30°
for your answer.
b
75°
c
B. Identify the type of triangle
a
and calculate angle a.
35° 105°

11. a. Right triangle
b. Obtuse
c. Acute
d. Obtuse

12. Number of right triangles: 20
abj, afj, dcp, dtp, jbk, jfk, gmk, hmk, gmn, hmn,
cpn, tpn, bfh, gfh, gth, cth, fbg, hbg, hgc, tgc
Number of isosceles triangles: 14
abf, dct, bkf, gkh, gnh, cnt, bkg, fkh, gnc, hnt
bhc, fkt, kgn, khn
Total number of triangles : 38
abj, afj, bjk, fjk, gkm, hkm, gnm, hnm, cnp, tnp,
cpd, tpd, bkg, fkh, gnc, hnt, baf, cdt, abk, afk, dcn,
dtn, bkf, gkh, gnh, cnt, bfh, gfh, fbg, hbg, ght, cht,
hgc, tcg, fgt, bhc, gkn, hkn

13. A. Angle a = 75°
Angle d = 105°
B. Obtuse triangle
Angle a = 40°

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