Warm-Up Exercises ANSWER x = 60; y = 60 ANSWER x = 35; y = 35 1. Find x and y. 2.

Slides:

Advertisements

Similar presentations

A B Q Chord AB is 18. The radius of Circle Q is 15. How far is chord AB from the center of the circle? 9 15 (family!) 12 x.

Advertisements

Warm-Up Exercises Simplify the expression. ANSWER 1 8 3π3π (9π)

You will use sides and angles to prove congruence. Essential Question: How can you use two sides and an angle to prove triangles congruent? 4.5 Prove Triangles.

Warm-Up Exercises 1. What is a translation? ANSWER a transformation that moves every point of a figure the same distance in the same direction ANSWER (7,

Chapter 10 Properties of Circles

Warm-Up Exercises 1. What measure is needed to find the circumference or area of a circle? 2. Find the radius of a circle with diameter 8 centimeters.

4.4 Prove Triangles Congruent by SSS

10.2 Arcs and Chords Central angle Minor Arc Major Arc.

MM2G3 Students will understand properties of circles. MM2G3 d Justify measurements and relationships in circles using geometric and algebraic properties.

Section 12.2 – 12.3 Chords & Arcs.

10.2 Find Arc Measures & 10.4 Use Inscribed Angles and Polygons

1. Solve 3x + 8 < 29. ANSWER x < 7 2. Solve 15 > –2x – 9.

Use Properties of Tangents

Arcs and Chords. Example 1: Applying Congruent Angles, Arcs, and Chords TV  WS. Find mWS. 9n – 11 = 7n n = 22 n = 11 = 88°  chords have.

1. 3x=x y+5y+66= x+14x= a 2 +16=25 Note: A diameter is a chord but not all chords are diameters.

1. The measure of the interior angles of a quadrilateral are 80º, 100º, 55º, and 5xº. Find the value of x. ANSWER Two supplementary angles have measures.

4.2 Apply Congruence and Triangles

MM2G3 Students will understand properties of circles. MM2G3 a Understand and use properties of chords, tangents, and secants as an application of triangle.

Unit 3: Circles & Spheres

Warm-Up Exercises SOLUTION EXAMPLE 1 Use the SSS Similarity Theorem Compare ABC and DEF by finding ratios of corresponding side lengths. Shortest sides.

Warm-Up a. mBD b. mACE c. mDEB d. mABC 140° 130° 230° 270°

Arc Lengths By the end of today, you will know about arcs and their measures and be able to do operations involving them.

4.6 Prove Triangles Congruent by ASA and AAS

MM2G3a Understand and use properties of chords, tangents, and secants as an application of triangle similarity.

1. Give the postulate or theorem that justifies why the triangles are similar. ANSWER AA Similarity Postulate 2. Solve = .

Chapter 10: Circles Find Arc Measures. Definitions Central Angle – of a circle is an angle whose vertex is the center of a circle Minor Arc – of.

6.2 Find Arc Measures. Vocabulary A central angle of a circle is an angle whose vertex is the center of the circle. A semicircle is an arc with endpoints.

Chapter 10.2 Notes: Find Arc Measures Goal: You will use angle measures to find arc measures.

10.2 Find Arc Measures Hubarth Geometry. The measures of a minor arc and a major arc depend on the central angle of the minor arc. Minor arc is less than.

C IRCLES (G.11 A /10.6) OBJ: SWB INTRODUCED TO BASIC TERMINOLOGY OF C IRCLES. SWBAT FIND THE MEASURES OF CENTRAL ANGLES, ARCS, ARC LENGTHS AND CIRCUMFERENCE.

EXAMPLE 1 Find measures of arcs RS a. RTS b. RST c. SOLUTION RS is a minor arc, so mRS = m RPS = 110 o. a. RTS is a major arc, so mRTS = 360 o 110 o =

10.3 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Apply Properties of Chords.

Find the area of a circle with the given measure.

6.2 Find Arc Measures Measuring Arcs

4.4 Proving Congruence – SSS and SAS What you’ll learn: 1.To use SSS Postulate to test for triangle congruence. 2.To use the SAS Postulate to test for.

Lesson 5.1, For use with pages

Chapter 10 Properties of Circles Mrs. Pullo February 29, 2016.

1. DC Tell whether the segment is best described as a radius,

Tell whether the segment is best described as a radius,

Chapter 10: Properties of Circles

In Exercises 1– 4, use A(0, 10), B(24, 0), and C(0, 0).

1. Find x and y. ANSWER x = 60; y = ANSWER x = 35; y = 35.

10.2 Find Arc Measures Hubarth Geometry.

Find Arc Measures Warm Up Lesson Presentation Lesson Quiz.

1. Find x and y. ANSWER x = 60; y = ANSWER x = 35; y = 35.

1. DC Tell whether the segment is best described as a radius,

EXAMPLE 1 Use congruent chords to find an arc measure

Lesson 8-4: Arcs and Chords

Obj: Use angle measures to find arc measures

10.2 Finding Arc Measures.

Geometry Chapter 12 Circles

1. Find the x-intercept of the graph of y = x2 – 11x a. -3,-5

1. Find x and y. 2. ANSWER x = 60; y = 60 ANSWER x = 35; y = 35.

EXAMPLE 1 Find measures of arcs

<APB is a Central Angle

EXAMPLE 1 Use congruent chords to find an arc measure

EXAMPLE 1 Identify special segments and lines

1. Write a congruence statement.

EXAMPLE 3 Identify congruent arcs

Drill Find x, if the semicircle arc of a circle is 3x + 30 degrees.

Warm Up 1. What percent of 60 is 18? 2. What number is 44% of 6?

Lesson 10-3: Arcs and Chords

EXAMPLE 1 Relate side length and angle measure

Sec. 12.2b Apply Properties of Chords p. 771

1. Find the length of AB for A(2, 7) and B(7, –5).

Goal: The learner to use angle measures to find arc measures.

Geometry Section I can find the measure of arcs in a circle give a central angle and a diameter.

________________________________________________

Warm Up 9.3, Day 1 Graph the circle

Presentation transcript:

Warm-Up Exercises ANSWER x = 60; y = 60 ANSWER x = 35; y = Find x and y. 2.

Warm-Up Exercises EXAMPLE 1 Find measures of arcs RS a. RTS b. RST c. SOLUTION RS is a minor arc, so mRS = m RPS = 110 o. a. RTS is a major arc, so mRTS = 360 o 110 o = 250 o. b. – Find the measure of each arc of P, where RT is a diameter. c. RT is a diameter, so RST is a semicircle, and mRST = 180 o.

Warm-Up Exercises EXAMPLE 2 Find measures of arcs A recent survey asked teenagers if they would rather meet a famous musician, athlete, actor, inventor, or other person. The results are shown in the circle graph. Find the indicated arc measures. Survey a. mAC SOLUTION a. mAC mAB =+ mBC = 29 o o = 137 o

Warm-Up Exercises EXAMPLE 2 Find measures of arcs b. mACD = mAC + mCD = 137 o + 83 o = 220 o A recent survey asked teenagers if they would rather meet a famous musician, athlete, actor, inventor, or other person. The results are shown in the circle graph. Find the indicated arc measures. Survey SOLUTION b. mACD

Warm-Up Exercises EXAMPLE 2 Find measures of arcs mADC mAC = 360 o – c. = 360 o – 137 o = 223 o A recent survey asked teenagers if they would rather meet a famous musician, athlete, actor, inventor, or other person. The results are shown in the circle graph. Find the indicated arc measures. Survey SOLUTION c. mADC

Warm-Up Exercises EXAMPLE 2 Find measures of arcs d. mEBD = 360 o – mED = 360 o – 61 o = 299 o d. mEBD A recent survey asked teenagers if they would rather meet a famous musician, athlete, actor, inventor, or other person. The results are shown in the circle graph. Find the indicated arc measures. Survey SOLUTION

Warm-Up Exercises GUIDED PRACTICE for Examples 1 and 2 Identify the given arc as a major arc, minor arc, or semicircle, and find the measure of the arc.

Warm-Up Exercises TQ is a minor arc, so m TQ = 120 o. GUIDED PRACTICE for Examples 1 and 2 1. TQ SOLUTION. QRT2 SOLUTION QRT is a major arc, so m QRT= 240 o.

Warm-Up Exercises GUIDED PRACTICE for Examples 1 and 2. TQR3 SOLUTION TQR is a semicircle, so m TQR = 180 o.. QS4 SOLUTION QS is a minor arc, so m QS = 160 o.

Warm-Up Exercises GUIDED PRACTICE for Examples 1 and 2. TS5 SOLUTION TS is a minor arc, so m TS = 80 o.. RST6 SOLUTION RST is a semicircle, so m RST = 180 o.

Warm-Up Exercises EXAMPLE 3 Identify congruent arcs Tell whether the red arcs are congruent. Explain why or why not. a. b. SOLUTION a. CD EF because they are in the same circle and mCD = mEF b. RS and TU have the same measure, but are not congruent because they are arcs of circles that are not congruent.

Warm-Up Exercises c. VX YZ because they are in congruent circles and mVX = mYZ. EXAMPLE 3 Identify congruent arcs Tell whether the red arcs are congruent. Explain why or why not. c. SOLUTION

Warm-Up Exercises GUIDED PRACTICE for Example 3 Tell whether the red arcs are congruent. Explain why or why not. 7. AB CD because they are in congruent circles and mAB = mCD. SOLUTION

Warm-Up Exercises GUIDED PRACTICE for Example 3 Tell whether the red arcs are congruent. Explain why or why not. 8. SOLUTION MN and PQ have the same measure, but are not congruent because they are arcs of circles that are not congruent.

Warm-Up Exercises Daily Homework Quiz Describe each figure as a minor arc, major arc or a semicircle. Find the arc measure. 1. BC ANSWERminor arc, 32 o

Warm-Up Exercises Daily Homework Quiz 2. Describe each figure as a minor arc, major arc or a semicircle. Find the arc measure. CBE ANSWERmajor arc, 212 o

Warm-Up Exercises Daily Homework Quiz 3. Describe each figure as a minor arc, major arc or a semicircle. Find the arc measure. BCE ANSWERsemicircle, 180 o

Warm-Up Exercises Daily Homework Quiz 4. Describe each figure as a minor arc, major arc or a semicircle. Find the arc measure. BC AE Explain why = ~. ANSWER BC AE = ~ m AFE = m BFC because the angles are vertical angles, so AFE BFC.Then arcs and are arcs that have the same measure in the same circle. By definition. = ~ AE BC

Warm-Up Exercises Daily Homework Quiz 5. ACD AC Two diameters of P are AB and CD. If m = 50, find m and m.. AD o ANSWER o 310 ; 130 o