quiz 1-3. What are angles as classified according to the number of congruent sides. 4-6. What are angles as classified according to the measures of their angles. 7-10. What are the secondary parts of a triangle.

Triangles LESSON 5

Polygon – a closed figure made up of many straight-sided figure. Review: Definition Polygon – a closed figure made up of many straight-sided figure. Copyright © 2000 by Monica Yuskaitis

Angle – two non-collinear rays that meet at a common end point. Definition Angle – two non-collinear rays that meet at a common end point. Copyright © 2000 by Monica Yuskaitis

Definition Right Angle – an angle whose measure is exactly 90°.Also define as an angle formed by 2 perpendicular lines. Copyright © 2000 by Monica Yuskaitis

Perpendicular lines– are two lines intersecting at right angles. Definition Perpendicular lines– are two lines intersecting at right angles. For example, ray EP & ray ET. P E T Copyright © 2000 by Monica Yuskaitis

Definition Degree – a unit of measurement of an angle or arc, represented by the symbol º. 30º Copyright © 2000 by Monica Yuskaitis

Triangle – a polygon with 3 angles and 3 straight sides. Definition Triangle – a polygon with 3 angles and 3 straight sides. Copyright © 2000 by Monica Yuskaitis

EXAMPLE TRIANGLE 3 SIDES. 3 VERTICES 3 ANGLES Copyright © 2000 by Monica Yuskaitis

BASIC PARTS S A SIDES AS, AM,SM VERTICES S, A, M ANGLES S, A. M M Copyright © 2000 by Monica Yuskaitis

Copyright © 2000 by Monica Yuskaitis TRIANGLES A ARE NAMED BY THEIR VERTICES. For example, The triangle shown can be named as SAM. S M Copyright © 2000 by Monica Yuskaitis

SECONDARY PARTS OF A TRIANGLE Every Triangle has secondary parts Copyright © 2000 by Monica Yuskaitis

SECONDARY PARTS OF A TRIANGLE ANGLE BISECTOR - Is a segment that DIVIDES (bisects) any angle of a triangle into 2 angles of equal measures. 20° 20° M N 30° 40° 30° 40° B G S AG, BN & SM are angle bisector of BAS.

SECONDARY PARTS OF A TRIANGLE ALTITUDE -The height of a triangle. Copyright © 2000 by Monica Yuskaitis

SECONDARY PARTS OF A TRIANGLE ALTITUDE - It is a segment drawn from any vertex of a triangle perpendicular to the opposite side. H C S N D

SECONDARY PARTS OF A TRIANGLE ALTITUDE EXAMPLE, SH, NC, OD are altitudes of SON. H C S N D Copyright © 2000 by Monica Yuskaitis

SECONDARY PARTS OF A TRIANGLE MEDIAN NOTE: like markings indicates congruent or equal parts. A B M C N Copyright © 2000 by Monica Yuskaitis

SECONDARY PARTS OF A TRIANGLE MEDIAN THUS, IN THE FIGURE OA = MA, OB = NB, MC = NC. A B M C N Copyright © 2000 by Monica Yuskaitis

SECONDARY PARTS OF A TRIANGLE A is the midpoint of MO. B is the midpoint of NO C is the midpoint of MN A B M C N Copyright © 2000 by Monica Yuskaitis

SECONDARY PARTS OF A TRIANGLE MEDIAN - Is a segment drawn from any vertex of a triangle to the MIDPOINT of the opposite side. A B M C N NA, MB & OC are median of MON. Copyright © 2000 by Monica Yuskaitis

Copyright © 2000 by Monica Yuskaitis Property of triangles The sum of all the angles equals 180º degrees. 60º 90º 30º Copyright © 2000 by Monica Yuskaitis

Copyright © 2000 by Monica Yuskaitis Property of triangles The sum of all the angles equals 180º degrees. 60º 90º 30º + 60º 180º 90º 30º Copyright © 2000 by Monica Yuskaitis

Copyright © 2000 by Monica Yuskaitis Property of triangles The sum of all the angles equals 180º degrees. 40º 90º 40º 50º + 180º 90º 50º Copyright © 2000 by Monica Yuskaitis

Copyright © 2000 by Monica Yuskaitis Property of triangles The sum of all the angles equals 180º degrees. 60º 60º 60º 60º + 180º 60º 60º Copyright © 2000 by Monica Yuskaitis

What is the missing angle? 70º 40º 70º ? ? + 180º 70º 70º Copyright © 2000 by Monica Yuskaitis

What is the missing angle? 90º 60º 30º ? ? + 30º 90º 180º Copyright © 2000 by Monica Yuskaitis

What is the missing angle? 60º 60º ? ? + 60º 180º 60º 60º Copyright © 2000 by Monica Yuskaitis

What is the missing angle? 30º 72º ? 78º ? + 78º 30º 180º Copyright © 2000 by Monica Yuskaitis

What is the missing angle? 40º 100º ? 40º ? + 40º 40º 180º Copyright © 2000 by Monica Yuskaitis

CLASSIFICATION of triangles WHAT CAN YOU SAY ABOUT THE SIDES OF A TRIANGLE? ACCORDING TO THE NUMBER OF CONGRUENT SIDES. 5 4 8 SCALENE TRIANGLE - No 2 sides are congruent. Copyright © 2000 by Monica Yuskaitis

CLASSIFICATION of triangles VERTEX LEG LEG 5 5 8 ISOCELES TRIANGLE - 2 sides are congruent. Copyright © 2000 by Monica Yuskaitis

PARTS of AN ISOSCELES triangles LEGS – are the congruent parts. VERTEX ANGLE 5 5 Base Angles Copyright © 2000 by Monica Yuskaitis

CLASSIFICATION of triangles B 8 8 F I 8 EQUILATERAL TRIANGLE - All sides are congruent. Copyright © 2000 by Monica Yuskaitis

CLASSIFICATION of triangles ACCORDING TO THEIR ANGLES. 85° 40° 55° ACUTE TRIANGLE - All angles are ACUTE. Copyright © 2000 by Monica Yuskaitis

CLASSIFICATION of triangles ACCORDING TO THEIR ANGLES. 90° 40° 50° RIGHT TRIANGLE - One angles is a right angle. Copyright © 2000 by Monica Yuskaitis

LEGS- are the other two sides. RIGHT TRIANGLE HYPOTENUSE- The longest side. It is the side opposite the 90º . LEGS- are the other two sides. hypotenuse leg leg

CLASSIFICATION of triangles ACCORDING TO THEIR ANGLES. 100° 50° 30° OBTUSE TRIANGLE - One angle is obtuse. Copyright © 2000 by Monica Yuskaitis

CLASSIFICATION of triangles ACCORDING TO THEIR ANGLES. 60° 60° 60° EQUIANGULAR TRIANGLE - All angles are congruent. Copyright © 2000 by Monica Yuskaitis

CLASSIFICATION of triangles ACCORDING TO THE NUMBER OF CONGRUENT SIDES SCALENE TRIANGLE ISOSCELES TRIANGLE EQUILATERAL TRIANGLE ACCORDING TO THEIR ANGLES ACUTE TRIANGLE RIGHT TRIANGLE OBTUSE TRIANGLE EQUIANGULAR TRIANGLE

True or false 1. An isosceles triangle can be an equilateral triangle. 2. An equilateral triangle can be an isosceles triangle. 3. A triangle can have two right angles. 4. An scalene triangle can be an equilateral triangle. 5. All angles of an equilateral triangle are acute. 6. All angles of an scalene triangle are acute. 7. The longest side of a right triangle is called the vertex. 8. Base angles of an isosceles triangle are always acute. 9. An equiangular triangle is also an equilateral triangle. 10. An scalene triangle can be a right triangle.

QUIZ Copyright © 2000 by Monica Yuskaitis

True or false 1. A triangle can be isosceles and acute. 2. A triangle can have two obtuse angles. 3. A triangle can be obtuse and scalene. 4. An scalene triangle can be an equilateral triangle. 5. A triangle can be right triangle and isosceles. 6. A triangle can have two right angles. 7. A triangle can have at most three acute angles. 8. A triangle can have at least one(1) acute angles. 9. An equilateral triangle is also an acute triangle. 10. An equiangular triangle can never be a right triangle.

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