Warm-up9.3 Special Right Triangles

Draw an equilateral triangle.

Label the sides as 2 cm and label the angles.

From a vertex draw the altitude.

Mark any congruent parts OR right angles.

Answers to 9.1 and 9.2 H.W.pg 481 #1-16 485 #1-7

9.3 Special Right Triangles

?hypotenusetheoflengththeiswhat

,23arethatlegshastriangleA4)

legs?theoflengththearewhat,26

oflengthhypotenuseahastriangleA3)

ConjecturesThe Pythagorean Theorem(C-81) In a right triangle, the sumof the squares of the lengths of the legs equals __________.

Converse of the PythagoreanTheorem(C-82) If the lengthsof the three sides of a triangle satisfy the Pythagoreanequation, then the triangle _____________________.

Isosceles Right Triangle Conjecture (C-83) In an isoscelesright triangle, if the legs have length l, then the hypotenusehas length _________.30°-60°-90° Triangle Conjecture (C-84) In a 30°-60°-90°triangle, if the shorter leg has length a, then the longer leghas length ____ and the hypotenuse has length ____ .

Directions for Practice Your Skills• This is the review for the 9.1 to 9.3 Quiz and Retest of Ch. 8.• #6 of the Practice Your Skills is not mandatoryHint: You will use Binomial Squared!• 12 and 13, you need to draw a line down the middle to

separate it into two special right triangles.• If you finish early, work on your card or the h.w. pg 494 1,2,6 and 9

9.1 to 9.3 Practice Your Skills

1. 21 cm 2. 23.9 cm 3. 8 ft.

4. 13 in. 5. 19 ft2 6. 29.5 cm

7. 49.7 cm2 8. 92.4 cm2

9. No 10. Yes 11. Yes

12. AC = AB = 82 area = 1,229 u2

13. AC = 60 AB = 116 area = 2,459 u2

1. A = 55 cm2 P = 36 cm 2. A = 950 m2 3. h = 24 ft4. 216 m2 5. 27 in 6.243. 96 cm2 7.8. 2,666 cm2

4.42230

22 cm68.37cm12