GEOMETRY



GEOMETRY

Lesson 3.1: CLASSIFYING TRIANGLES BY THEIR ANGLES AND SIDES

NOTES

Objectives: 1) To identify and classify triangles by angles 2) To identify and classify triangles by sides

College Readiness Standards:

1. Exhibit knowledge of basic angle properties and special sums of angle measures. (Score range 20-23)

2. Use several angle properties to find an unknown angle measure. (Score Range 24 - 27)

|A triangle is a closed plane figure bounded by three |2) An equiangular triangle is an acute triangle with |Classifying Triangles according to the Length of their |

|line segments. |all angles congruent. |Sides |

|[pic] | |1) A scalene triangle has no equal sides. |

|ABC is a triangle having three sides and three interior |600 |8 |

|angles. The symbol for a triangle is ∆, so triangle ABC | |5 |

|is written as ∆ABC. | |7 6 10 |

| | | |

|The sides of ∆ABC are the line segments AB, BC and AC. | |4 |

| |600 600 | |

|The angles of ∆ABC are [pic]ABC, [pic]BCA, and | |2) An equilateral triangle has all sides equal. |

|[pic]CAB. | | |

| |3) A right triangle has one angle equal to 90°.  That|600 |

|[pic]ABC can be denoted by [pic]B. |is, one angle is a right angle. | |

|[pic]BCA can be denoted by [pic]C. |[pic] | |

|[pic]CAB can be denoted by [pic]A. |Note: | |

| |The side opposite the right angle is called the |600 600|

|A point where two of the sides of a triangle meet is |hypotenuse. | |

|called the vertex of the triangle. The plural of |The hypotenuse is the longest side of the triangle |All angles of an equilateral triangle are 60°. |

|“vertex” is vertices. The vertices of ∆ABC are the |(which can be verified with a ruler). |Note: |

|points A, B, and C. | |To show that the sides of an equilateral triangle have |

| | |the same length, we place identical marks on the sides |

|Types of Triangles |4) An obtuse triangle has one angle greater than 90º. |of the triangle. |

|Triangles can be classified according to the length of |That is, one angle is obtuse. |To show that the angles of an equilateral triangle are |

|their sides and the size of their angles. | |equal in size, we place identical curves on each angle. |

| |A |3) An isosceles triangle has two sides equal. |

|Classifying Triangles according to the Size of their |980 |A |

|Angles | | |

| | | |

|1) An acute triangle has all angles less than 90º (i.e.|B 580 240 | |

|all three angles are acute). |C | |

| | |B C |

| |∆ABC is an obtuse-angle triangle as [pic]BAC is an |The angles opposite the equal sides are equal. |

| |obtuse angle. |[pic]B = [pic]C |

|780 | | |

| | |Note: side BC is the base |

| | | |

|430 590 | | |

GEOMETRY

Classwork 3.1.1: CLASSIFYING TRIANGLES BY ANGLES AND SIDES

Name: ________________________________ Period: ____ Date: ___________ Score:

Objectives: 1) To identify and classify triangles by angles 2) To identify and classify triangles by sides

College Readiness Standards:

1. Exhibit knowledge of basic angle properties and special sums of angle measures. (Score range 20-23)

2. Use several angle properties to find an unknown angle measure. (Score Range 24 - 27)

|Describe each triangle by as many of the following words|5) |9) Supply the correct numbers to complete each sentence |

|as apply: acute, obtuse, right, equiangular, scalene, |1200 |as you view each type of triangle. |

|isosceles, or equilateral. | | |

| | |In an obtuse triangle, there are _______ acute angle(s),|

|1) |300 300 |_______ right angle(s) and |

|350 | |_______ obtuse angles. |

| | | |

| |_____________________________ |In an acute triangle, there are _______ acute angle(s), |

| | |_______ right angle(s) and |

|550 | |_______ obtuse angles. |

| | | |

|_____________________________ |6) |In a right triangle, there are _______ acute angle(s), |

| | |_______ right angle(s) and |

| |1490 |_______ obtuse angles. |

| |14.5 14 | |

|2) | |In an equiangular triangle, there are |

| |150 160 |_______ acute angle(s), _______ right angle(s) and |

| |14.6 |_______ obtuse angles. |

|1350 | | |

| | |10) Determine whether each statement is always, |

| |______________________________ |sometimes, or never true in a triangle. |

|_____________________________ | | |

| | |A right triangle is ______________scalene. |

| | | |

|3) |7) 12 |An obtuse triangle is _____________isosceles. |

| | | |

|600 | |An equilateral triangle is ____________a right triangle.|

| |17 5 | |

| | |An equilateral triangle is___________ isosceles. |

| | | |

|600 600| |An acute triangle is _____________isosceles. |

| | | |

| |_____________________________ |A scalene triangle is |

|_____________________________ | |_____________obtuse. |

| | | |

| | | |

| |8) 500 | |

|4) | | |

| |650 650 | |

|5 | | |

|3 | | |

| | | |

| |___________________________ | |

| | | |

|4 | | |

| | | |

| | | |

|_____________________________ | | |

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