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OTCQ

OTCQ. RGT is adjacent to angle TGL. If m RGL = 100 ◦ and m TGL = 20 ◦ , What is m RGT?. OTCQ. RGT is adjacent to angle TGL. If m RGL = 100 ◦ and m TGL = 20 ◦ , What is m RGT?. R.

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OTCQ

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  1. OTCQ RGT is adjacent to angle TGL. If m RGL = 100 ◦ and m TGL = 20 ◦, What is m RGT?

  2. OTCQ RGT is adjacent to angle TGL. If m RGL = 100 ◦ and m TGL = 20 ◦, What is m RGT? R 20 ◦ T G 80 ◦ L

  3. Aims 1-6 & 1-7 How do we define angles and triangles? NY GG 31, GG 32, GG 33, GG 35, GG 28 Read 1-6 and 1-7 do problems 18 -25 on page 22.

  4. 1-6 & 1-7 objectives 1. SWBAT name angles and angle parts. 2. SWBAT define: congruent angles, complimentary angles, supplementary angles and adjacent angles Bisector of an angle Perpendicular line Distance from a point to a line 3. SWBAT add angles. 4. SWBAT define a triangle and its parts.

  5. An angle consists of two different rays that have the same initial point. The rays are the sides of the angle. The initial point A is the vertex of the angle. The angle that has rays AB and AC as sides may be named BAC, CAB, or A. B sides Vertex A C

  6. The set of all points between the sides of the angle is the interior of an angle. The exterior of an angleis the set of all points outside the angle.

  7. Angle Name R, SRT, TRS, or 1 If the point is the vertex of more than one angle, you must use all three points to name the angle. The middle point is always the vertex.

  8. The measure of A is denoted by mA. The measure of an angle can be approximated using a protractor, using units called degrees(°). BAC has a measure of 50°, which can be written as mBAC = 50°. B C A

  9. Angle Relationships M W E R U S Congruent Angles: Angles with equal measures in degrees. MSU EWR or USM RWE

  10. Angle Relationships Complementary Angles: Two angles are called complementary angles if the sum of their degree measurements equals 90° degrees. Supplementary Angles: Two angles are called supplementary angles if the sum of their degree measurements equals 180° degrees.

  11. Angle Relationships • Adjacent Angles: Share a vertex and a common side but no interior points. • Bisector of an angle: a ray that divides the angle into two congruent angles. is the angle bisector.

  12. Two lines that intersect at a 90 ◦angle (right angle) are Perpendicular lines. Boxed vertex means 90 ◦ What are perpendicular lines?

  13. The shortest distance from a point to a line will always be the distance of the perpendicular line from the point to the line. Boxed vertex means 90 ◦

  14. Adding Angles • When you want to add angles, use the notation m1, meaning the measure of 1. • If you add m1 + m2, what is your result? m1 + m2 = 58. m1 + m2 = mADC also. Therefore, mADC = 58.

  15. Congruent Angles that measure the same in degrees are congruent. PET TEJ LEP JEL J E T L P Symbol for congruent

  16. Congruent Explain why the angles are congruent. PET TEJ LEP JEL J E T L P Symbol for congruent

  17. Congruent They are all 90◦ PET TEJ LEP JEL J E T L P Symbol for congruent

  18. Congruent Segments that measure the same in inches, feet, miles, milimeters, centimeters, meters, or kilometers are called congruent. ___ ___ AT PC A T P C Symbol for congruent

  19. 1-6 & 1-7 objectives CHECK UP 1. SWBAT name angles and angle parts. 2. SWBAT define: congruent angles, complimentary angles, supplementary angles and adjacent angles Bisector of an angle Perpendicular line Distance from a point to a line 3. SWBAT add angles. 4. NEXT:SWBAT define a triangle and its parts.

  20. Polygon: A closed plane figure formed by three or more line segments that meet only at their endpoints.

  21. Triangle: a polygon with exactly 3 sides. Types of Triangles: Equilateral all 3 sides and angles are congruent. Also called Equiangular. Isosceles Triangle— 2 or 3 sides/angles are congruent Scalene—no sides or angles are congruent

  22. Triangle Parts: 3 vertices: A, B, C. 3 line segments: __ __ __ BC , CA & AB Any 2 line segments in a triangle that share a common endpoint are called adjacent sides. __ CB is the opposite side of endpoint A __ __ CA and BA share endpoint A, so they are adjacent sides. __ __ CB and BA share endpoint B, so they are adjacent sides. __ __ BC and CA share endpoint C, so they are adjacent sides.

  23. EQUILATERAL is EQUIANGULAR • 3 congruent 60◦ acute angles (“equiangular”). • 3 congruent line segments. (“equilateral” ). • Acute. • Can’t be right • Also isosceles because at least 2 sides/angles are congruent. • Each line segment is a side.

  24. Isosceles Triangles need only 2 congruent sides/angles. Vertex Angle • The 2 congruent sides are called legs. Green dashes means congruent. • The noncongruent side is called the base. No green dashes. • The 2 congruent angles are called base angles. Blue arc means congruent. • The noncongruent angle is called the vertex angle. No blue arcs. leg leg Base Base Base Angle Angle

  25. A right triangle with 2 congruent sides/angles, is an isosceles right triangle. its base angles are each 45◦ The red side is both a hypotenuse and a base. The boxed 90◦ right angle is the vertex angle. Green dashes mean congruent. Blue arcs mean congruent. ISOCELES Right Triangle 45◦ base Hypotenuse angle base leg leg 45 ◦ 90◦ Base angle vertex

  26. Acute Triangle: an acute triangle has 3 acute angles.Could be equilateral/equiangular (all = 60◦).Could be isosceles ∆ or scalene ∆ but never a right and never an obtuse ∆.

  27. 1 right angle Obtuse Triangle: has one obtuse angle. Right Triangle Right and Obtuse triangles are never acute or equilateral, but can be isosceles (have 2 congruent sides/angles).

  28. Red represents the hypotenuse of a right triangle. The blue sides that form the right angle are the legs. Right Triangle hypotenuse leg leg

  29. What is this? leg base leg

  30. What is this? An isosceles triangle. leg base leg

  31. Quick Algebra Review

  32. Commutative Property Commutative Property of Addition: a + b = b + a Commutative Property of Multiplication: ab = ba Examples 2 + 3 = 5 = 3 + 2 3• 4 = 12 = 4 • 3 The commutative property does not work for subtraction or division!!!!!!!!

  33. Associative Property Associative property of Addition: (a + b) + c = a + (b + c) Associative Property of Multiplication: (ab) c = a (bc) Examples (1 + 2) + 3 = 1 + (2 + 3) (2 • 3) • 4 = 2 • (3 • 4) The associative property does not work for subtraction or division!!!!!

  34. Identity Properties 1) Additive Identity a + 0 = a 2) Multiplicative Identity a • 1 = a

  35. Inverse Properties 1) Additive Inverse (Opposite) a + (-a) = 0 2) Multiplicative Inverse (Reciprocal)

  36. Multiplicative Property of Zero a • 0 = 0 (If you multiply by 0, the answer is 0.)

  37. The Distributive Property Any factor outside of expression enclosed within grouping symbols, must be multiplied by each term inside the grouping symbols. Outside left or Outside right a(b + c) = ab + ac (b + c)a = ba + ca a(b - c) = ab – ac (b - c)a = ba - ca Time permitting start homework

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