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Which Dimensions Can Create More Than One Triangle?

Written By Monday, February 14, 2022 Add Comment Edit

Lesson 10 Drawing Triangles (Part 2)

Let's draw some more triangles.

Learning Targets:

  • Given ii side lengths and ane angle measure, I can describe different triangles with these measurements or bear witness that these measurements determine i unique triangle or no triangle.

10.1 Using a Compass to Estimate Length

  1. Draw a 40^\circ angle.
  2. Use a compass to brand certain both sides of your bending have a length of five centimeters.
  3. If you connect the ends of the sides you drew to make a triangle, is the tertiary side longer or shorter than 5 centimeters? How can you employ a compass to explicate your reply?

x.2 Revisiting How Many Tin You Draw?

Use the applet to draw triangles.

  1. Draw as many different triangles as you tin with each of these sets of measurements:

    1. Ane bending measures xl^\circ , ane side measures 4 cm and one side measures v cm.
    2. Two sides measure 6 cm and one angle measures 100^\circ .

  2. Did either of these sets of measurements determine i unique triangle? How practise you know?

10.3 Iii Angles

Use the applet to describe triangles. Sides can overlap.

  1. Draw as many different triangles as you tin with each of these sets of measurements:
    1. Ane angle measures 50^\circ , one measures 60^\circ , and one measures 70^\circ .
    2. One bending measures 50^\circ , one measures 60^\circ , and one measures 100^\circ .
  2. Did either of these sets of measurements make up one's mind one unique triangle? How practise you know?

Are you prepare for more?

Using only the indicate, segment, and compass tools provided, create an equilateral triangle. You are only successful if the triangle remains equilateral while dragging its vertices around.

Lesson 10 Summary

A triangle has vi measures: three side lengths and three angle measures.

If we are given iii measures, then sometimes, there is no triangle that can be fabricated. For example, in that location is no triangle with side lengths 1, 2, 5, and in that location is no triangle with all three angles measuring 150^\circ .

Sometimes, merely ane triangle can be made. By this nosotros hateful that any triangle nosotros make volition be the same, having the aforementioned six measures. For case, if a triangle tin be made with three given side lengths, and then the corresponding angles will have the aforementioned measures. Another example is shown hither: an bending measuring 45^\circ between two side lengths of six and 8 units. With this information, i unique triangle can be made.

Sometimes, 2 or more than different triangles can be fabricated with three given measures. For example, here are two different triangles that can be made with an angle measuring 45^\circ and side lengths half-dozen and 8. Notice the angle is non between the given sides.

Three pieces of information about a triangle's side lengths and angle measures may determine no triangles, one unique triangle, or more than 1 triangle. It depends on the information.

Lesson x Practice Problems

  1. A triangle has sides of length 7 cm, 4 cm, and v cm. How many unique triangles can be fatigued that fit that clarification? Explain or bear witness your reasoning.

  2. A triangle has one side that is 5 units long and an next angle that measures 25^\circ . The ii other angles in the triangle measure ninety^\circ and 65^\circ . Consummate the two diagrams to create two different triangles with these measurements.

  3. Is it possible to make a triangle that has angles measuring 90 degrees, 30 degrees, and 100 degrees? If so, draw an example. If non, explain your reasoning.

  4. Segments CD , AB , and FG intersect at betoken Due east . Angle FEC is a correct angle. Identify any pairs of angles that are complementary.

  5. Match each equation to a step that volition help solve the equation for x .

    1. 3x=\text-four
    2. \text-four.5 = x-3
    3. three=\frac {\text{-}10}{3}
    4. \frac13=\text-3x
    5. 10-\frac{1}{3}=0.4
    6. 3+x=8
    7. \frac{x}{3}=15
    8. 7=\frac{ane}{3}+10
    1. Add \frac13 to each side.
    2. Add together \frac {\text{-}1}{3} to each side.
    3. Add 3 to each side.
    4. Add \text-iii to each side.
    5. Multiply each side by 3.
    6. Multiply each side by \text-three .
    7. Multiply each side by \frac13 .
    8. Multiply each side by \frac {\text{-}1}{3} .
    1. If you lot eolith $300 in an account with a half dozen% interest rate, how much will be in your business relationship afterwards 1 yr?
    2. If y'all leave this money in the account, how much will exist in your account after 2 years?

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Source: https://access.openupresources.org/curricula/our6-8math/en/grade-7/unit-7/lesson-10/index.html

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