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GeoGebraClasse GeoGebra
GeoGebra

UNIT 4 LESSON 1: TRIANGLES AND THEIR SIDE LENGTHS

Auteur :Rachel Turner, Tim Brzezinski, Mark Beckwith, Steve Phelps
Thème :Angles, Triangles

REMEMBER:

In triangle ABC, m∠BAC = 50°. If m∠ACB = 30°, then the triangle is _________  triangle.

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  • A
  • B
  • C
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In triangle ABC, m∠BAC = 50°. If m∠ABC = 40°, then the triangle is ________  triangle.

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  • A
  • B
  • C
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In triangle ABC, m∠BAC = 50°. If triangle ABC is isosceles, and AB = 6 and BC = 4, then AC = _______.

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  • A
  • B
  • C
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ANALYZING OBTUSE TRIANGLES

ANALYZING OBTUSE TRIANGLES QUESTION

CAN A TRIANGLE HAVE TWO OBTUSE ANGLES?

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If triangle LMN has an obtuse angle at vertex M, which statements could be true? Check all that apply.

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  • A
  • B
  • C
  • D
  • E
  • F
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Triangle XYZ is a right triangle with the right angle at vertex Y. Angle X must be_______.

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  • A
  • B
  • C
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Angle Z must be_______.

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  • A
  • B
  • C
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The sum of angles X and Z must be ________  90°. 

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  • A
  • B
  • C
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ANALYZING POSSIBLE SIDE LENGTHS OF TRIANGLES

Determine whether the given triple represents the side lengths of an acute, a right, or an obtuse triangle. Use the Pythagorean Theorem to help you decide. Use the given checkboxes to check your answer. Use the New Triple button to receive a new triple.

TRIANGLE INEQUAILTY THEOREM

Interact with the applets below. Adjust the side lengths of the triangle by sliding the sliders or typing in the box. You are looking to see which lengths of sides create a triangle and which ones do not.

CAN YOU MAKE A TRIANGLE?

Can you make a triangle with these side lengths? a = 5, b = 3 and c = 2

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  • A
  • B
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Can you make a triangle with these side lengths? a = 3, b = 4 and c = 5

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  • B
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Can you make a triangle with these side lengths? a = 3, b = 7 and c = 3

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  • A
  • B
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Can you make a triangle with these side lengths? a = 6, b = 4 and c = 3

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  • A
  • B
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Can you make a triangle with these side lengths? a = 5, b = 4 and c = 4

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  • B
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What do you notice about these triangle lengths?

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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 < _______

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  • B
  • C
  • D
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TRIANGLE ANGLE AND SIDE LENGTH RELATIONSHIPS

Move the blue slider to change the shape of the triangle and move the black slider to see what happens. Then move the blue slider again to see what happens to the relationship between angles and their opposite sides. What seems to be always true? If it helps, click the angle tool to measure the angles in degrees and the length tool to measure the length of the sides. There is a video below the applet if you do not remember how.

HOW TO MEASURE

Record the side each angle corresponds to after you move the slider.

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What do you notice about the relationship between the side lengths of triangles and their angles opposite them?

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ISOSCELES TRIANGLE CONSTRUCTION VIDEO

CONSTRUCTING AN ISOSCELES TRIANGLE

THESE ARE THE STEPS TO CONSTRUCTING AN ISOSCELES TRIANGLE:
  1. Create a line segment
  2. Created the perpendicular bisector to that segment.
  3. Create a point on the perpendicular bisector.
  4. 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?

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CONSTRUCT AN EQUALATERAL TRIANGLE

THESE ARE THE STEPS I USED TO CONSTRUCT AN EQUALATERAL TRIANGLE:
  1. Create a line segment
  2. Create a circle with the center at one endpoint of the line segment, the length of the radius the length of the line segment.
  3. 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.
  4. 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?

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REMEMBER:

UNDER WHICH ANGLE CONDITIONS COULD A TRIANGLE EXIST? (CHECK ALL THAT APPLY)

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  • A
  • B
  • 2 ACUTE ANGLES, 1 RIGHT ANGLE

  • C
  • 1 ACUTE ANGLE, 1 RIGHT ANGLE, 1 OBTUSE ANGLE

  • D
  • 1 ACUTE ANGLE, 2 OBTUSE ANGLES

  • E
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    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?

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    • A
    • B
    • She is correct. The remaining angle of the triangle measures less than 90 degrees.

  • C
  • She is incorrect. The angles measure greater than 90 degrees so the triangle is obtuse.

  • D
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    In triangle RST, m∠R > m∠S + m∠T. Which must be true of triangle RST? Check all that apply.

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    • A
    • B
    • C
    • D
    • E
    • F
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