Warm-up with 4.5 other congruence shortcuts For 1 -3 tell whether it is possible (YES or No) to draw a triangle with the given side lengths. 1) 7 in., 5 in., 10 in. ________ 2) 9cm, 7cm, 21 cm _______ 3) 5 ft., 4ft., 9ft. ______ Arrange the letters from greatest value to least value. 4) _______________ 5) ____________________
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Warm-up with 4.5 other congruence shortcuts For 1 -3 tell whether it is possible (YES or No) to draw a triangle with the given side lengths. 1) 7 in.,
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Warm-upwith 4.5 other congruence shortcuts
For 1 -3 tell whether it is possible (YES or No) to draw a trianglewith the given side lengths.
1) 7 in., 5 in., 10 in. ________ 2) 9cm, 7cm, 21 cm _______ 3) 5 ft., 4ft., 9ft. ______
Arrange the letters from greatest value to least value.
4) _______________ 5) ____________________
Student of the day!Block 4
Student of the day!Block 5
Student of the day!Block 6
H.W. Answers to pg pg 160 # 1- 5 and #10pg 224 #4-9, and #12 - 17
H.W. Answers
Algebra Review pg 212 - 214Properties of equality a = b
Addition property a + c = b + c
Subtraction property a – c = b – c
Multiplication Property ac = bc Division Property
Use the properties above, in addition to Distributive Property and Combining Like Terms to do 2 column proof for Algebra Equations.
c
b
c
a
Can’t forget Distributive Property and Combining Like
Terms
We are not covering 3.5, on constructing parallel lines.
Solve the following. Show your steps and writeyour supporting properties in a proof format
Steps Supporting Reaons4x + 8 = -4 (2x – 7) + 4
Another 2 column proof
Steps Supporting Reasons
4
1
5
3
2
xx
4.5 Congruence ShortcutsSSS (Side-Side-Side) when three sides of one triangle arecongruent to another three sides in another triangle than thetriangles are congruent.
SAS (Side-Angle-Side) when two sides and an included angleof one triangle are congruent to another triangle, then thetriangles are congruent.
There are two other combinations that work to prove thattwo triangles are congruent.
ASA InvestigationThis is not a construction.1) Draw a 4 inch segment.2) On one end, measure a 60 degree angle and draw the
other side of the angle.3) On the other end of the 4 inch segment draw a 40 degree
angle and draw the other side of the angle.4) Notice the two sides of the 60 degree and 40 degree
angle meet. This is your triangle.
Other congruence conjecturesSAA (Side-Angle-Angle) works too.
What doesn’t work: AAA (these triangles are similar)not necessarily congruent.
SSA also doesn’t work.
4.5 More Congruence Shortcuts
ConjecturesC-25 ASA Congruence Conjecture – If two angles and an included sideare congruent to two angles and an included side in another trianglethen, ________________________.
C-26 SAA Congruence Conjecture – If two angles and a non-includedside, are congruent to two angles and a non-included side in anothertriangle then, ____________________.
• Prepare for 3.1 to 3.5 and 4.1 to 4.5 Quiznext block
Constructions: Know how to copy an angle, a segment.Know how to construct a perpendicular bisector (findingmidpoint), the shortest distance from a point to aLine, altitude, median.Know how to bisect an angle.Ch. 4 Material: Know how to use conjectures to solve formissing angles in triangles and parallel lines. Know yourcongruence conjectures and all conjectures. Know when twotriangles are congruent.