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Warm up

Simplify: 1. √72 2. √84 3. √36 Solve: √(39x + 40) = x (hint: square both sides first then factor) (x + 1) = √(x + 3) (hint: square both sides then factor). Warm up. ± 6 √2 ±2 √21 ±6 40 and -1 -2 and 1 No. AAA is not a postulate or theorem. Yes. AAS.

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Warm up

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  1. Simplify: • 1. √72 • 2. √84 • 3. √36 • Solve: • √(39x + 40) = x (hint: square both sides first then factor) • (x + 1) = √(x + 3) (hint: square both sides then factor) Warm up • ±6 √2 • ±2 √21 • ±6 • 40 and -1 • -2 and 1 • No. AAA is not a postulate or theorem. • Yes. AAS. • No. SSA is not a postulate or theorem. Tell whether each pair of triangles are congruent. How do you know?

  2. Constructions You need: • Paper • Pencil • Straightedge • Compass

  3. Segment construction

  4. Try another one • Draw segment LM • Follow the steps from before to create L’M’

  5. Let’s construct an angle • Using your straightedge create an acute angle. Label the vertex P. • To construct it’s duplicate: • Draw a ray with your straightedge with endpoint P’ • Use the compass with pointy on P, and swoop • DO NOT CHANGE THE COMPASS and swoop again with the pointy on P’ • Label the points of intersection A and W and A’, W’ – although we are not sure where A’ is. • With the compass, measure AW, do a mini-swoop. Transfer that measurement to A’W’ and mini-swoop. • The point of intersection, between your two mini-swoops is A’. • Draw the ray P’A’

  6. Let’s do it again • Draw an obtuse angle with vertex A • Follow the steps from before using M and C as the points on the rays.

  7. Constructing an equilateral triangle

  8. Let’s do it again • Draw the equilateral triangle ΔLMN • Using the steps from before, duplicate it.

  9. Constructing a triangle given 3 sides. • Draw 3 segments on your paper: BL=2”, LP=3”, PB=4” • Beneath or on the side, draw a ray with endpoint P, longer than 4”. • Transfer the length of segment PB. • Measure segment LP…mini swoop… transfer… miniswoop • Label • Measure segment BL… mini swoop… transfer… miniswoop • Label • Connect

  10. Let’s do it again • Draw ΔLMN • Given: LM=6”, MN=2”, LN=3” • Using the steps from before, duplicate it. The sum of the 2 shortest sides must be greater than the length of the longest side. Ahhhhh…. What can we say about the side length of a triangle?

  11. Constructing an angle bisector

  12. You guessed it…Let’s make another one! Draw angle EF with your straightedge and bisect it with the compass and straightedge.

  13. Please remember… • DO NOT erase your swoops. It is only by a teacher looking at those that they can tell you know what you’re doing. • NO SWOOPS = NO SCORE (no joke)

  14. Your assignment Pg 264; 5-15

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