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# Triangles 101

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### Triangles 101

1. 1. Triangular Shape<br />Electromagnetism<br />The Lost Continent of Atlantis<br />Portal to Another Dimension<br />
2. 2. TRIANGLES<br />
3. 3. Definition<br />A set of points is a triangle if and only if it consists of the figure formed by three segments connecting three noncollinear points.<br /><ul><li>Each of the three noncollinear points is called a vertex.
4. 4. Thesegments are called the sides.</li></ul>vertex<br />side<br />side<br />vertex<br />vertex<br />side<br />
5. 5. Naming a Triangle and its parts<br />Triangle ABC / ΔABC<br />Angles: A, B, & C<br />Sides: AB, BC, & CA<br />a, b, & c<br />B<br />c<br />a<br />A<br />C<br />b<br />Note: Naming = Consecutive vertices (preferably clockwise)<br />
6. 6. Triangle Classification (accdg. to sides)<br /> pg 129 <br />ISOSCELES<br />At least 2 sides congruent<br />SCALENE<br />No sides congruent<br />EQUILATERAL<br />All sides congruent<br />Using the Geoboards<br />
7. 7. Triangle Classification (accdg. to angles)<br /> pg 129 <br />ACUTE<br />3 acute angles<br />RIGHT<br />1 right angle<br />┌<br />EQUIANGULAR<br />All angles congruent<br />OBTUSE<br />1 obtuse angle<br />
8. 8. Paper-folding Investigation<br />B<br />Draw a triangle similar in shape to the ΔABC. Cut it out.<br />Slide point A along AC toward point C until the fold passes through point B. The crease intersects AC at point D. Unfold the triangle.<br />A<br />C<br />B<br />C<br />D<br />A<br />B<br />A<br />C<br />D<br />
9. 9. <ul><li>Bring point A to point D and crease.
10. 10. Bring points B and C to point D and crease.</li></ul>B<br />A<br />C<br />D<br />B<br />A<br />C<br />D<br />What appears to be true about the sum of the measures of these angles three angles?<br />
11. 11. pg 110 - 111 <br />The sum of the measures of angles of a triangle is 180o.<br />B<br />4<br />5<br />3<br />B<br />A<br />C<br />1<br />2<br />A<br />C<br /> A + B + C = 180o<br />
12. 12. Sample Problems<br />The angles of a triangle are in a ratio 3:4:5. Find the measures of all the angles.<br />2.<br /> pg 111 - 112 <br />(2x)o<br />(4x-8)o<br />(5x-10)o<br />
13. 13. TRUE or FALSE?<br /> pg 114 <br />If two angles of one triangle are congruent to two angles of a second triangle, then the third angles are congruent.<br />Each angle of an equiangular triangle measures 60o.<br />In a triangle, there can be at most one right triangle, or at most one obtuse angle.<br />The acute angles of a right triangle are complementary.<br />
14. 14. Exterior Angles of a Triangle<br /> pg 116 - 117 <br />ΔABC has been extended to form exterior angles:<br />1, 2, & 3.<br />Each exterior angle has an adjacent interior angle and two remote interior angles.<br />Example:<br />Exterior angle:<br />Adjacent interior angle:<br />Two remote angles:<br />A<br />1<br />6<br />3<br />4<br />5<br />B<br />C<br />2<br />2<br />4<br />6 & 5<br />
15. 15. Protractor investigation (exterior and remote interior angles)<br />The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.<br /> 1 = 4 + 5<br /> 2 = 5 + 6<br /> 3 = 4 + 6 <br /> pg 117 <br />A<br />5<br />1<br />6<br />4<br />3<br />4<br />5<br />B<br />C<br />2<br />
16. 16. Sample Problems: Solve for x.<br />1.<br />2. <br /> pg 117 <br />40o<br />xo<br />23o<br />84o<br />7xo<br />5xo<br />
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