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, ____________________.

H.W. Assignment• Algebra Review pg 214 #2- 16• 4.5 pg 230 #4 – 16

• 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.

Common quiz mistakes FORM A3.

FORM B3.

Using linear pair to copy an obtuse angle