We’re going to do two sections today Measuring segments 1.4 – Measuring angles Please begin on the warm up. Thanks

Let’s grade your homework

1.3 Measuring Length

How do you measure distance on a number line? What is the distance between -2 and 35 What is the distance between -2 and -7 What is the distance between 5 and 17 What is the distance between 0 and -5 What is the distance between 10 and Notice that all the DISTANCES ARE POSITIVE! What mathematical operation makes all answers positive? ABSOLUTE VALUE!!!

♥On a number line, the distance between the coordinates a and b is |a-b| or |b-a|. ♥This will give you the measure of the segment. Measuring length a b WRITE THIS DOWN

Notation for MEASURE of a segment mXY or XY If you use the bar, use the m. If you don’t use the bar, don’t use the m In this notation, we are talking about the LENGTH of the segment NOT the segment itself X Y Z mXY = |-3 - 0| = |-3| = 3 XZ = |-3 - 4| = |-7| = 7

CONGRUENT Means the same size and same shape The congruent symbol is = ~ Means the same size and same shape The congruent symbol is = ~ A B C D AB CD ~ = AB C D E

Segment Congruence Postulate ♥If two segments are congruent, then they have the same measure.

AB C D E Important notation If AC BD then AC = BD ~ = This says: if the segments are CONGRUENT then the measures are EQUAL. Without the bar means NUMBER AC is a NUMBER AC is NOT

Segment Addition Postulate If point R is between points P and Q, then PR + RQ = PQ P R Q A B C 3 5 AB + BC = AC = AC 8 = AC X + 3x + 1 = 25 4x + 1 = 25 4x = 24 X = 6 A B C x 3x + 1 AC = 25

1.4 Measuring Angles

Angle Addition Postulate m< PQS + m< SQR = m< PQR P Q S R Which one makes sense? A B

Angle Congruence Postulate ♥If two angles have the same measure, then they are congruent.

Acute Angle – An angle whose measure is less than 90°. Right Angle – An angle whose measure is exactly 90°. Obtuse Angle – An angle whose measure is greater than 90° and less than 180°. Straight Angle - An angle whose measure is exactly 180°. Reflex Angle – An angle whose measure is greater than 180° and less than 360°. Angles

COMPLEMENTARY Angles – Exactly two angles whose sum is 90°. Each angle is a COMPLEMENT of the other. SUPPLEMENTARY Angles = Exactly two angles whose measure is 180°. Each angle is a SUPPLEMENT of the other. A 60° 120° C 30° B Complementary angles are < A and < B < A and < B are complements of each other < A and < C are supplementary angles < A and < C are supplements of each other Are you doing ok?

Linear Pair Property If two angles form a line, they are a linear pair AND are supplementary. 125° 55°

Your assignment 1.3 – pgs 24-26; 9-55 odds 1.4 – pgs 31-33; 7-49 odds