UNIT 4 LESSON 1: TRIANGLES AND THEIR SIDE LENGTHS
REMEMBER:
In triangle ABC, m∠BAC = 50°.
If m∠ACB = 30°, then the triangle is _________ triangle.
In triangle ABC, m∠BAC = 50°. If m∠ABC = 40°, then the triangle is ________ triangle.
In triangle ABC, m∠BAC = 50°. If triangle ABC is isosceles, and AB = 6 and BC = 4, then AC = _______.
ANALYZING OBTUSE TRIANGLES
ANALYZING OBTUSE TRIANGLES QUESTION
CAN A TRIANGLE HAVE TWO OBTUSE ANGLES?
If triangle LMN has an obtuse angle at vertex M, which statements could be true? Check all that apply.
Triangle XYZ is a right triangle with the right angle at vertex Y.
Angle X must be_______.
Angle Z must be_______.
The sum of angles X and Z must be ________ 90°.
ANALYZING POSSIBLE SIDE LENGTHS OF TRIANGLES
TRIANGLE INEQUAILTY THEOREM
CAN YOU MAKE A TRIANGLE?
Can you make a triangle with these side lengths? a = 5, b = 3 and c = 2
Can you make a triangle with these side lengths? a = 3, b = 4 and c = 5
Can you make a triangle with these side lengths? a = 3, b = 7 and c = 3
Can you make a triangle with these side lengths? a = 6, b = 4 and c = 3
Can you make a triangle with these side lengths? a = 5, b = 4 and c = 4
What do you notice about these triangle lengths?
The distance between Lincoln, NE, and Boulder, CO, is about 500 miles. The distance between Boulder, CO, and a third city is 200 miles.
Assuming the three cities make a triangle on the map, which values represent the possible distance, d, in miles, between Lincoln, NE, and the third city?
300 < d < _______
TRIANGLE ANGLE AND SIDE LENGTH RELATIONSHIPS
HOW TO MEASURE
Record the side each angle corresponds to after you move the slider.
What do you notice about the relationship between the side lengths of triangles and their angles opposite them?
ISOSCELES TRIANGLE CONSTRUCTION VIDEO
CONSTRUCTING AN ISOSCELES TRIANGLE
- Create a line segment
- Created the perpendicular bisector to that segment.
- Create a point on the perpendicular bisector.
- Create line segments to the point on the perpendicular bisector to the endpoints of the line segment.
CONSTRUCTING AN ISOSCELES TRIANGLE ANOTHER WAY
ISOSCELES TRIANGLE QUESTION
An isosceles triangle is a triangle with at least two congruent sides. Why are the triangles above in the videos isosceles triangles?
CONSTRUCT AN EQUALATERAL TRIANGLE
- Create a line segment
- Create a circle with the center at one endpoint of the line segment, the length of the radius the length of the line segment.
- Create another circle with the center at the other endpoint of the line segment, the length of the radius the length of the line segment.
- Create two more line segments connecting the endpoints of the line segment to the intersection of the circles.
Why is the triangle constructed above an equilateral triangle?
REMEMBER:
UNDER WHICH ANGLE CONDITIONS COULD A TRIANGLE EXIST? (CHECK ALL THAT APPLY)
Triangle DEF contains two congruent acute angles. The sum of the measures of the two congruent acute angles is greater than 90 degrees. Anna concludes that the triangle must be an acute triangle. Which best describes her conclusion?
In triangle RST, m∠R > m∠S + m∠T. Which must be true of triangle RST? Check all that apply.