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Lines and Angles Calter, Section 6-1 Define the following terms: Line Line segment Angle Vertex Perpendicular lines Parallel lines In the picture to the right, we can designate the angle in any of the following ways: angle ABC angle CBA angle B angle θ We can also use the symbol or to mean ‘angle’ i) Draw and define an acute angle ABC . ii) Draw and define an right angle DEF . iii)Draw and define an obtuse angle GHI . iv) Draw and define a straight angle JKL . v) Draw and define complementary angles. vi) Draw and define supplementary angles. Lines, Angles and Triangles 1 Angles between intersecting lines In the figure, which angles are equal? Which angles are supplementary? Parallel lines There are certain angle properties that apply ONLY to parallel lines. If there are two parallel lines intersected by a third line p, the line p is called the transversal. In the figure, which angles are equal. Which angles are supplementary? Triangles Calter, Section 6-2 Draw and define the following triangles by angle measure: i) Right triangle ii) Acute triangle iii) Obtuse triangle Lines, Angles and Triangles 2 Draw and define the following triangles by side length: i) Scalene triangle ii) Acute triangle iii) Equilateral triangle Define the Sum of the Interior Angles in a triangle property: Define the Exterior angle of a Triangle property: Define the Isosceles Triangle Theorem: Congruent Triangles Two triangles (or any other polygons, for that matter) are said to be congruent if the angles and sides of one are equal to the angles and sides of the other. We can say that 2 triangles are congruent if they satisfy one of the following conditions: - Two sides and the contained angle of one triangle equal two sides and the contained angle of the other triangle (“Side-Angle-Side Theorem”) - Two angles and any side of one triangle are equal to two angles and the contained side of the other triangle (“Angle-Angle-Side Theorem”) Lines, Angles and Triangles 3 Similar Triangles Two triangles are said to be similar if they have the same shape, even if one triangle is larger than the other. The angles of one of triangle must equal the angles of the other triangle. Their sides will be proportional. Polygons Define the Sum of the Interior Angles of a Polygon Theorem: Practise Find the measures of all the angles in the figures below: 1) 2) a 65º b c z d 3) e y f z 4) 70º g h j l z i k zm 35º z Lines, Angles and Triangles 4 5) 6) 70o 58o 15 cm 9 cm 3 cm 30o 4 cm 7. In question 6, find the lengths of all the sides 8. If two angles in a triangle measure 34 and 65 degrees, what is the measure of the third angle? 9. Joseph wishes to find the length of a lake. He makes the measurements shown. Calculate the length of the lake. 65 m 52 m 65o 72 m 65o 10. CHALLENGE: Tina wants to find the height of a tree. She places a meter stick vertically on the ground and notices that the stick casts a shadow 0.4m long. The tree casts a shadow 2m long. How high is the tree? Lines, Angles and Triangles 5