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We’re going to do two sections today. 1.3 - Measuring segments 1.4 – Measuring angles

We’re going to do two sections today. 1.3 - Measuring segments 1.4 – Measuring angles. Please begin on the warm up. Thanks. Let’s grade your homework. 1.3 Measuring Length. -3 -2 -1 0 1 2 3 4 5 6 7. ABSOLUTE VALUE!!!.

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We’re going to do two sections today. 1.3 - Measuring segments 1.4 – Measuring angles

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  1. We’re going to do two sections today. 1.3 - Measuring segments1.4 – Measuring angles Please begin on the warm up. Thanks

  2. Let’s grade your homework

  3. 1.3Measuring Length

  4. -3 -2 -1 0 1 2 3 4 5 6 7 ABSOLUTE VALUE!!! How do you measure distance on a number line? What is the distance between -2 and 3 5 What mathematical operation makes all answers positive? 5 What is the distance between -2 and -7 12 What is the distance between 5 and 17 5 What is the distance between 0 and -5 What is the distance between 10 and -3 13 Notice that all the DISTANCES ARE POSITIVE!

  5. b a Measuring length • 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. WRITE THIS DOWN

  6. -3 -2 -1 0 1 2 3 4 5 6 7 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

  7. ~ = A B E C D 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

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

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

  10. P R Q AC = 25 A B C 3 5 A B C x 3x + 1 Find the measure of each segment and CHECK YOUR ANSWER Segment Addition Postulate If point R is between points P and Q, then PR + RQ = PQ X + 3x + 1 = 25 4x + 1 = 25 4x = 24 X = 6 AB + BC = AC 3 + 5 = AC 8 = AC

  11. 1.4 Measuring Angles

  12. S P R Q Which one makes sense? B A Angle Addition Postulate m< PQS + m<SQR = m<PQR <A + <B = 85° Or m <A + m <B = 85°

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

  14. Angles • 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°.

  15. Are you doing ok? • 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. 30° B 120° C A 60° 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

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

  17. Your assignment 1.3 – pgs 25-27; 17-47odds 1.4 – pgs 33-35; 11-39 odds

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