mon 11/4. boot-up 11.4.13 / 6 min. 2) solve for each variable:1) name any 2 of the 4 pythagorean...
TRANSCRIPT
Boot-Up 11.4.13 / 6 min.
2) Solve for each variable:1) Name any 2 of the 4 Pythagorean Triples discussed in class:
a) ___ : ___: ___
b) ___ : ___: ___
Boot-Up 11.6.13 / 6 min.
2) Solve for each variable:1) Name any 3 of the 5 Congruence Theorems:
1) ______
2) ______
3) ______
4) ______
5) ______
Boot-Up 11.4.13 / 6 min.
2) Solve for each variable:1) Name any 2 of the 4 Pythagorean Triples discussed in class:
a) ___ : ___: ___
b) ___ : ___: ___
Boot-Up 11.4.13 / 6 min.
2) Solve for each variable:1) Name any 2 of the 4 Pythagorean Triples discussed in class:
a) ___ : ___: ___
b) ___ : ___: ___
Today’s Objective:
*SWBAT = Student Will Be Able To
6.1.1: SWBAT identify s by first determining that the s are ~ & that the ratio of corresponding sides is 1.
6.1.2: TSW develop shortcuts.
Fields that use trigonometry or trigonometric functions include:Astronomy (especially for locating apparent positions of celestial objects, in which spherical trigonometry is essential) and hence navigation (on the oceans, in aircraft, and in space), music theory, acoustics, optics, analysis of financial markets, electronics, probability theory, statistics, biology, medical imaging (CAT scans and ultrasound), pharmacy, chemistry, number theory (and hence cryptology), seismology, meteorology, oceanography, many physical sciences, land surveying and geodesy, architecture, phonetics, economics, electrical engineering, mechanical engineering, civil engineering, computer graphics, cartography, crystallography & game development.
OK, but what’s in it for me?
As you can see, even though side BC = BD , this side length is able to swivel such that 2 non-congruent s are created even though they have 2 sides and a , non-included . (SSA)
ABC ABD
The 2 s are NOT congruent 3-86
There are 2 things you have to do to prove congruence. They are:
1) Prove Similarity. (That they’re the Same Shape.)
2) Prove Side Lengths have a common ratio of 1. (That they’re the Same Size.)
6-2a
If you prove similarity by virtue of congruence, how many sides do you have to prove are congruent to prove s are ?
Two figures are congruent if they meet both the following conditions:•The two figures are similar, and•Their side lengths have a common ratio of 1
If 2 sides & the included of one are to the corresponding parts of another , the s are .
1) SAS (Side-Angle-Side)
6-12
If 2 s and the included side of 1 are to the corresponding parts of another , the s are .
3) ASA (Angle-Side-Angle)
If 2 s and the non-included side of one are to the corresponding parts of another , the s are .
AAS
4) AAS (Angle-Angle-Side)
If the hypotenuse & leg of one right are to the corresponding parts of another right , the right s are .
HL (Right s Only)
5)
As you can see, even though side BC = BD , this side length is able to swivel such that 2 non-congruent s are created even though they have 2 sides and a , non-included . (SSA)
ABC ABD
The 2 s are NOT congruent 3-86
5-2a
y3=tan 60
y3=1.732
=1 y 1.732 3
y 5.196=
y1=tan 60
y1=1.732
=1 y 1.732 1
y 1.732=Hey, Bub: Divide these rises (5.196 1.732), what do you get? Now divide the runs…
5-2a
a2 + b2 = c2
32 + y2 = 62
9 + y2 = 36
y2 = 27
y2 = 27
y = 5.196
a2 + b2 = c2
12 + y2 = 22
1 + y2 = 4
y2 = 3
y2 = 3
y = 1.732
Did we get the same answers both ways?
Boot-Up 11.6.13 / 6 min.
2) Solve for each variable:1) Name any 3 of the 5 Congruence Theorems:
1) ______
2) ______
3) ______
4) ______
5) ______
Today’s Objective:
*TSW= The Student Will
6.1.4:
1) TSW extend their use of flowcharts to document facts.
2) TSW practice identifying pairs of s and will contrast congruence arguments with similarity arguments.
29.2
4
2) Solve for each variable:1) Name any 3 of the 5 Congruence Theorems:
1) ______
2) ______
3) ______
4) ______
5) ______
Boot-Up 11.7.13 / 6 min.
Today’s Objective:
*SWBAT = Student Will Be Able To
6.1.5: SWBAT recognize the converse relationship between conditional statements, & will then investigate the relationship between the truth of a statement & the truth of its converse.
2-46
Same Side Interiors Supplementary
Rianna says something’s wrong with this picture. Do you agree?
What is the sum of s x & y?
Conditional statements that have this relationship are called converses.
6-41c
Write the converse of the conditional statement below: If lines are parallel, then corresponding angles are equal.
Triangles congruent → corresponding sides are congruent.
6-42a
True False
Converse Statement: _______________________________
True False
Triangles congruent → corresponding angles are congruent.
6-42c
True False
Converse Statement: _______________________________
True False
A shape is a rectangle → the area of the shape is b h.
6-42d
True False
Converse Statement: _______________________________
True False
Today’s Objective:
*SWBAT = Student Will Be Able To
6.2.2: SWBAT review area & perimeter of a , Trigonometry, Pythagorean Theorem, & the Triangle Angle Sum Theorem.