Triangles 101
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1. Triangles can be classified based on their sides as isosceles, scalene, or equilateral. The sum of the interior angles of any triangle is always 180 degrees. 2. The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles. 3. True or false questions about triangle properties include: if two angles are congruent then the third must be; each angle of an equiangular triangle is 60 degrees; a triangle can have at most one right or obtuse angle.
Triangles 101
- 1. Triangular ShapeElectromagnetismThe Lost Continent of AtlantisPortal to Another Dimension
- 2. TRIANGLES
- 3. DefinitionA set of points is a triangle if and only if it consists of the figure formed by three segments connecting three noncollinear points.Each of the three noncollinear points is called a vertex.
- 4. Thesegments are called the sides.vertexsidesidevertexvertexside
- 5. Naming a Triangle and its partsTriangle ABC / ΔABCAngles: A, B, & CSides: AB, BC, & CAa, b, & cBcaACbNote: Naming = Consecutive vertices (preferably clockwise)
- 6. Triangle Classification (accdg. to sides) pg 129 ISOSCELESAt least 2 sides congruentSCALENENo sides congruentEQUILATERALAll sides congruentUsing the Geoboards
- 7. Triangle Classification (accdg. to angles) pg 129 ACUTE3 acute anglesRIGHT1 right angle┌EQUIANGULARAll angles congruentOBTUSE1 obtuse angle
- 8. Paper-folding InvestigationBDraw a triangle similar in shape to the ΔABC. Cut it out.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.ACBCDABACD
- 9. Bring point A to point D and crease.
- 10. Bring points B and C to point D and crease.BACDBACDWhat appears to be true about the sum of the measures of these angles three angles?
- 11. pg 110 - 111 The sum of the measures of angles of a triangle is 180o.B453BAC12AC A + B + C = 180o
- 12. Sample ProblemsThe angles of a triangle are in a ratio 3:4:5. Find the measures of all the angles.2. pg 111 - 112 (2x)o(4x-8)o(5x-10)o
- 13. TRUE or FALSE? pg 114 If two angles of one triangle are congruent to two angles of a second triangle, then the third angles are congruent.Each angle of an equiangular triangle measures 60o.In a triangle, there can be at most one right triangle, or at most one obtuse angle.The acute angles of a right triangle are complementary.
- 14. Exterior Angles of a Triangle pg 116 - 117 ΔABC has been extended to form exterior angles:1, 2, & 3.Each exterior angle has an adjacent interior angle and two remote interior angles.Example:Exterior angle:Adjacent interior angle:Two remote angles:A16345BC2246 & 5
- 15. Protractor investigation (exterior and remote interior angles)The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles. 1 = 4 + 5 2 = 5 + 6 3 = 4 + 6 pg 117 A5164345BC2
- 16. Sample Problems: Solve for x.1.2. pg 117 40oxo23o84o7xo5xo