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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