Review Solving Linear Equations Solve 5 x8 2

Review – Solving Linear Equations • Solve: (5 x+8) - (2 x - 9) = 38

More Algebra Review Problems

7. 4 Measuring Segments and Angles Geometry Gonzales

Postulate • 1 -5 Ruler Postulate – The points of a line can be put into oneto-one correspondence with the real numbers so that the distance between any two points is the absolute value of the difference of the corresponding numbers.

Definition • Congruence – Two segments with the same length are congruent Segments. – Symbol Represents length or distance Same Size Same Shape

STANDARD 17 A B C AB + BC = AC • If B is between A and C then AB + BC = AC. • If AB + BC = AC, then B is between A and C. PRESENTATION CREATED BY SIMON PEREZ. All rights reserved SEGMENT ADDITION POSTULATE.

Postulate • 1 -6 Segment Addition Postulate –If three points A, B, and C are collinear and B is between A and C, then AB+BC = AC

Find the length for AB and BC if AC = 60 and AB = 4 x + 6 and BC= 6 x + 14. (B is between A and C) STANDARD 17 Applying Segment Addition Postulate: A C B AB + BC = AC 4 x +6 + 6 x + 14 = 60 4 x + 6 + 14 = 60 10 x + 20 = 60 -20 Now finding AB and BC: AB = 4 x + 6 BC = 6 x + 14 = 4( 4 ) + 6 = 6( 4 ) + 14 = 16 + 6 = 24 + 14 = 22 = 38 10 x = 40 10 10 x=4 Verifying the solution: 22 + 38 = 60 60 = 60 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

Find the length of EF and FG if EG = 80 and EF = 3 x + 8 and FG= 7 x + 12. (F is between E and G) STANDARD 17 Applying Segment Addition Postulate: E G F EF + FG = EG 3 x +8 + 7 x + 12 = 80 3 x + 7 x + 8 + 12 = 80 10 x + 20 = 80 -20 Now finding EF and FG: EF = 3 x + 8 FG = 7 x + 12 = 3( 6 ) + 8 = 7( 6 ) + 12 = 18 + 8 = 42 + 12 = 26 = 54 10 x = 60 10 10 x=6 Verifying the solution: 26 + 54 = 80 80 = 80 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

Definitions • Midpoint – Is a point that divides a segment into two congruent segments. • Bisect – Two cut into two equal parts

STANDARD 17 MIDPOINT OF A SEGMENT: A C B If we have segment AC, and we place point B at the same distance from point A than from Point C, then: AB BC Means congruent AB = BC and then point B is THE MIDPOINT OF SEGMENT AC. Point B is also BISECTING segment AC, because it is dividing it into two halves. PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

AC is bisected by ED. AB= 6 X + 8 and BC=4 X + 18. Find the length for AC. STANDARD 17 A D B C E AB BC AB = BC 6 X + 8 = 4 X + 18 -8 -8 6 X = 4 X + 10 -4 X 2 X = 10 2 2 X=5 Now finding AB: AB = 6 X + 8 Applying Segment Addition Postulate: AC = AB + BC = 6( 5 ) + 8 AC = AB + BC = 30 + 8 AC = 38 + 38 = 38 AC = 76 Since AB = BC BC = 38 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

RT is bisected by VU. RS= 8 X + 4 and ST=4 X + 28. Find the length for RT. STANDARD 17 R V S T U RS ST RS = ST 8 X + 4 = 4 X + 28 -4 -4 8 X = 4 X + 24 -4 X 4 X = 24 4 4 X=6 Now finding RS: RS = 8 X + 4 Applying Segment Addition Postulate: RT = RS + ST = 8( 6 ) + 4 RT = RS + ST = 48 + 4 RT = 52 + 52 = 52 RT = 104 Since RS = ST ST = 52 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

STANDARD 17 DISTANCE FORMULA in a number line is given by: |a – b| Find measure of DE, and EH: -6 -4 D -2 0 2 4 6 8 12 H E DE = |-2 – (-6)| 10 EH = |12 – (-2)| = |-2 + 6| = |12 + 2| = |4| = |14| =4 = 14 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

STANDARD 17 DISTANCE FORMULA in a number line is given by: |a – b| Find measure of RT, and QT: -6 -4 -2 0 2 4 R 6 8 Q RT = |12 – (-6)| QT = |12 – 6| = |12 + 6| = |18| =6 = 18 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved 10 12 T

STANDARD 17 MIDPOINT FORMULA in a number line is given by: a+b 2 Find Midpoint Q of RT: -6 -4 R -2 0 2 4 6 8 Q 6 -6 + 12 = 2 2 =3 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved 10 12 T

STANDARD 17 MIDPOINT FORMULA in a number line is given by: a+b 2 Find Midpoint R of KL: -4 -2 K 0 2 4 6 8 10 R 10 -4 + 14 = 2 2 =5 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved 12 14 L

Definitions • Angle ( All the ways you can name this angle: ) < TBQ – Is formed by two rays with the same endpoint. < QBT <B • The rays are the sides of the angle • The endpoints form the vertex of the angle. B <2 T 2 Q

Angle symbol: • 2 rays that share the same endpoint (or initial point) Sides – the rays XY & XZ Y 5 X Z Named <YXZ, <ZXY (vertex is always in the middle), or <X (if it’s the only <X in the diagram). Vertex – the common endpoint; X Angles can also be named by a #. (<5)

There are 3 different <B’s in this diagram; therefore, none of them should be called <B. A <B ? D B C

Angle Measurement • m<A means the “measure of <A” • Measure angles with a protractor. • Units of angle measurement are degrees (o). • Angles with the same measure are congruent angles. • If m<A = m<B, then <A <B.

Postulate 1 -7: Protractor Post. • The rays of an angle can be matched up with real #s (from 1 to 180) on a protractor so that the measure of the < equals the absolute value of the difference of the 2 #s. 55 o 20 o m<A = 55 -20 = 35 o

Postulate • 1 -7 Protractor Postulate:

Types of Angles • Acute angle – Measures between 0 o & 90 o • Right angle – Measures exactly 90 o • Obtuse angle – Measures between 90 o & 180 o • Straight angle – Measures exactly 180 o

Find the measure and classify the angle according to its measure.

Interior or Exterior? • B is ______ in the interior • C is ______ in the exterior on the < • D is ______ B C A D

Post. 1 -8: Angle Addition post. • If P is in the interior of <RST, then m<QRP + m<PRS = m<QRS. S P If m<QRP=5 xo, m<PRS=2 xo, & m<QRS=84 o, find x. 5 x+2 x=84 Q 7 x=84 x=12 m<QRP=60 o m<PRS=24 o R

Measuring Angles LESSON 1 -6 Additional Examples Name the angle below in four ways. The name can be the number between the sides of the angle: The name can be the vertex of the angle: 3. G. Finally, the name can be a point on one side, the vertex, and a point on the other side of the angle: AGC, CGA. Quick Check

Measuring Angles LESSON 1 -6 Additional Examples Suppose that m 1 = 42 and m ABC = 88. Find m 2. Use the Angle Addition Postulate to solve. m 1+m 2=m ABC Angle Addition Postulate. 42 + m 2 = 88 Substitute 42 for m m 2 = 46 Subtract 42 from each side. 1 and 88 for m ABC. Quick Check

Ex: Angle Addition Postulate • Let m<AOC= 7 x – 2 , m<AOB = 2 x+8, and m<BOC = 3 x+14, find x and all angle measures. A B C O D

Assignment • 1 -4 – Pg. 29 1 -28; 42 -45; 75 -76; 87 -97 • Algebra Review – Solving Equations – Pg. 24 2 -20 evens only