Lesson 4 Menu 1.Refer to the figure. The radius of is 35, = 80, LM = 45, and LM  NO. Find. 2.Find. 3.Find the measure of NO. 4.Find the measure of NT.

Slides:

Advertisements

Similar presentations

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 10–3) CCSS Then/Now New Vocabulary Theorem 10.6: Inscribed Angle Theorem Proof: Inscribed Angle.

Advertisements

10.4 Inscribed Angles.

Splash Screen. Over Lesson 10–3 5-Minute Check 1.

Lesson  Theorem 89: If two inscribed or tangent- chord angles intercept the same arc, then they are congruent.

Inscribed Angles Section 10.5.

Find the perimeter and area of the parallelogram. Round to

10.2– Find Arc Measures. TermDefinitionPicture Central Angle An angle whose vertex is the center of the circle P A C.

Warm – up 2. Inscribed Angles Section 6.4 Standards MM2G3. Students will understand the properties of circles. b. Understand and use properties of central,

10.3 Arcs and Chords & 10.4 Inscribed Angles

Chapter 10.4 Notes: Use Inscribed Angles and Polygons

Inscribed Angles By the end of today, you will know what an inscribed angle is and how to find its measure.

Inscribed Angles. An inscribed angle has a vertex on a circle and sides that contain chords of the circle. In, C,  QRS is an inscribed angle. An intercepted.

Inscribed Angles 10.3 California State Standards

Lesson 1 Menu 1.Name a radius. 2.Name a chord. 3.Name a diameter. 4.Find if m  ACB = Write an equation of the circle with center at (–3, 2) and.

Lesson 4 Menu 1.Determine whether the quadrilateral shown in the figure is a parallelogram. Justify your answer. 2.Determine whether the quadrilateral.

Arcs and Chords Chapter 10-3.

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 10–2) NGSSS Then/Now Theorem 10.2 Proof: Theorem 10.2 (part 1) Example 1: Real-World Example:

Circle GEOMETRY Radius (or Radii for plural) The segment joining the center of a circle to a point on the circle. Example: OA.

Over Lesson 10–3 A.A B.B C.C D.D 5-Minute Check 1 80.

10.3 Inscribed Angles. Definitions Inscribed Angle – An angle whose vertex is on a circle and whose sides contain chords of the circle Intercepted Arc.

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 10–3) NGSSS Then/Now New Vocabulary Theorem 10.6: Inscribed Angle Theorem Proof: Inscribed Angle.

Section 10.3 Inscribed Angles. Inscribed Angle An angle whose vertex is on a circle and whose sides contain chords of the circle Inscribed Angle.

Inscribed Angles Inscribed Angles – An angle that has its vertex on the circle and its sides contained in chords of the circle. Intercepted – An angle.

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 10–3) Then/Now New Vocabulary Theorem 10.6: Inscribed Angle Theorem Proof: Inscribed Angle Theorem.

5-Minute Check on Lesson 10-3 Transparency 10-4 Click the mouse button or press the Space Bar to display the answers. The radius of ⊙ R is 35, LM  NO,

Concept. Example 1 Use Inscribed Angles to Find Measures A. Find m  X. Answer: m  X = 43.

10-4 Inscribed Angles You found measures of interior angles of polygons. Find measures of inscribed angles. Find measures of angles of inscribed polygons.

Splash Screen. Vocabulary inscribed angle intercepted arc.

Lesson 2 Menu 1.Find the measure of an interior angle of a regular polygon with 10 sides. 2.Find the measure of an interior angle of a regular polygon.

Lesson 5 Menu 1.Find the area of the figure. Round to the nearest tenth if necessary. 2.Find the area of the figure. Round to the nearest tenth if necessary.

Lesson 3 Menu 1.The quadrilaterals are similar. Write a similarity statement and find the scale factor of the larger quadrilateral to the smaller quadrilateral.

Find the area of the figure. Round to the nearest tenth if necessary.

Lesson 8-1: Circle Terminology

Lesson 7 Menu Warm-up Problems State the property that justifies each statement. 1.2(LM + NO) = 2LM + 2NO. 2.If m  R = m  S, then m  R + m  T = m 

Complete the statement about and justify your answer. AB  ? AD  ?

Lesson 3 Menu 1.In, BD is a diameter and m  AOD = 55. Find m  COB. 2.Find m  DOC. 3.Find m  AOB. 4.Refer to. Find. 5.Find.

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 10–4) NGSSS Then/Now New Vocabulary Example 1:Identify Common Tangents Theorem Example.

Can the measure of 5, 7, and 8 be the lengths of the sides of a triangle? Can the measures 4.2, 4.2, and 8.4 be the lengths of the sides of a triangle?

Geometry/Trig 2Name: __________________________ Fill In Notes – 9.4 Chords and Arcs Date: ___________________________ Arcs can be formed by figures other.

Lesson 5 Menu Five-Minute Check (over Lesson 2-4) Main Ideas and Vocabulary Targeted TEKS Example 1: Solve an Equation with Variables on Each Side Example.

4.5 – Prove Triangles Congruent by ASA and AAS In a polygon, the side connecting the vertices of two angles is the included side. Given two angle measures.

GeometryGeometry Lesson 6.1 Chord Properties. Geometry Geometry Angles in a Circle In a plane, an angle whose vertex is the center of a circle is a central.

Inscribed Angles By the end of today, you will know what an inscribed angle is and how to find its measure.

Section 10-3 Inscribed Angles. Inscribed angles An angle whose vertex is on a circle and whose sides contain chords of the circle. A B D is an inscribed.

Inscribed Angles LESSON 10–4. Lesson Menu Five-Minute Check (over Lesson 10–3) TEKS Then/Now New Vocabulary Theorem 10.6: Inscribed Angle Theorem Proof:

Arcs and Chords Chapter Lesson 2 MI/Vocab central angle arc minor arc major arc semicircle Recognize major arcs, minor arcs, semicircles, and central.

A. 60 B. 70 C. 80 D. 90.

Aim: How do we prove triangles congruent using the Angle-Angle-Side Theorem? Do Now: In each case, which postulate can be used to prove the triangles congruent?

Inscribed Angles By the end of today, you will know what an inscribed angle is and how to find its measure.

Secants, Tangents and Angle Measures

Three ways to prove triangles congruent.

Five-Minute Check (over Lesson 10–3) Then/Now New Vocabulary

Class Greeting.

Section 6.2 More Angle Measures in a Circle

Objectives Prove certain triangles are similar by using AA, SSS, and SAS. Use triangle similarity to solve problems.

Inscribed Angles Chapter 10-4.

LESSON 10–4 Inscribed Angles.

LESSON 10–4 Inscribed Angles.

Circles and inscribed angles

Five-Minute Check (over Lesson 9–4) Mathematical Practices Then/Now

Section 10.4 Use Inscribed Angles And Polygons Standard:

Inscribed Angles.

More Angle-Arc Theorems

11.5 Inscribed Angles.

Five-Minute Check (over Lesson 9–3) Mathematical Practices Then/Now

Presentation transcript:

Lesson 4 Menu 1.Refer to the figure. The radius of is 35, = 80, LM = 45, and LM  NO. Find. 2.Find. 3.Find the measure of NO. 4.Find the measure of NT. 5.Find the measure of RT.

Lesson 4 MI/Vocab intercepted Find measures of inscribed angles. Find measures of angles of inscribed polygons.

Lesson 4 TH1

Lesson 4 Ex1 Measures of Inscribed Angles

Lesson 4 Ex1 Measures of Inscribed Angles Arc Addition Postulate Simplify. Subtract 168 from each side. First determine Divide each side by 2.

Lesson 4 Ex1 Measures of Inscribed Angles So, m

Lesson 4 Ex1 Measures of Inscribed Angles

A.A B.B C.C D.D Lesson 4 CYP1 A.30 B.60 C.15 D.120

A.A B.B C.C D.D Lesson 4 CYP1 A.110 B.55 C.125 D.27.5

A.A B.B C.C D.D Lesson 4 CYP1 A.30 B.80 C.40 D.10

A.A B.B C.C D.D Lesson 4 CYP1 A.110 B.55 C.125 D.27.5

A.A B.B C.C D.D Lesson 4 CYP1 A.110 B.55 C.125 D.27.5

Lesson 4 TH2

Lesson 4 Ex2 Proof with Inscribed Angles Given: Prove: ΔPJK  ΔEHG

Lesson 4 Ex2 Proof with Inscribed Angles Proof: Statements Reasons 1. Given If 2 chords are, corr. minor arcs are Inscribed angles of arcs are Right angles are congruent. 6. ΔPJK  ΔEHG 6. AAS Definition of intercepted arc

Lesson 4 CYP2 Choose the best reason to complete the following proof. Given: Prove: ΔCEM  ΔHJM

Lesson 4 CYP2 1. Given 2. ______ 3. Vertical angles are congruent. 4. Radii of a circle are congruent. 5. ASA Proof: Statements Reasons ΔCEM  ΔHJM

Lesson 4 CYP2 1.A 2.B 3.C 4.D A.Alternate Interior Angle Theorem B.Substitution C.Definition of  angles D.Inscribed angles of  arcs are .

Lesson 4 Ex3 Inscribed Arcs and Probability

Lesson 4 Ex3 Inscribed Arcs and Probability The probability that is the same as the probability of L being contained in.

1.A 2.B 3.C 4.D Lesson 4 CYP3 A.B. C.D.

Lesson 4 TH3

Lesson 4 Ex4 Angles of an Inscribed Triangle

Lesson 4 Ex4 Angles of an Inscribed Triangle ΔUVT and ΔUVT are right triangles. m  1 = m  2 since they intercept congruent arcs. Then the third angles of the triangles are also congruent, so m  3 = m  4. Angle Sum Theorem Simplify. Subtract 105 from each side. Divide each side by 3.

Lesson 4 Ex4 Angles of an Inscribed Triangle Use the value of x to find the measures of Given Answer:

Lesson 4 Ex5 Draw a sketch of this situation. Angles of an Inscribed Quadrilateral

Lesson 4 Ex5 Angles of an Inscribed Quadrilateral To find we need to know To find first find Inscribed Angle Theorem Sum of arcs in circle = 360 Subtract 174 from each side.

Lesson 4 Ex5 Angles of an Inscribed Quadrilateral Inscribed Angle Theorem Substitution Divide each side by 2. Since we now know three angles of a quadrilateral, we can easily find the fourth. m  Q + m  R + m  S + m  T=360360° in a quadrilateral m  T=360Substitution m  T=78Subtraction Answer: m  S = 93; m  T = 78

Lesson 4 TH4