Presentation is loading. Please wait.

Presentation is loading. Please wait.

Splash Screen.

Similar presentations


Presentation on theme: "Splash Screen."— Presentation transcript:

1 Splash Screen

2 Five-Minute Check (over Lesson 10–3) CCSS Then/Now New Vocabulary
Theorem 10.6: Inscribed Angle Theorem Proof: Inscribed Angle Theorem (Case 1) Example 1: Use Inscribed Angles to Find Measures Theorem 10.7 Example 2: Use Inscribed Angles to Find Measures Example 3: Use Inscribed Angles in Proofs Theorem 10.8 Example 4: Find Angle Measures in Inscribed Triangles Theorem 10.9 Example 5: Real-World Example: Find Angle Measures Lesson Menu

3 A. 60 B. 70 C. 80 D. 90 5-Minute Check 1

4 A. 40 B. 45 C. 50 D. 55 5-Minute Check 2

5 A. 40 B. 45 C. 50 D. 55 5-Minute Check 3

6 A. 40 B. 30 C. 25 D. 22.5 5-Minute Check 4

7 A. 24.6 B. 26.8 C. 28.4 D. 30.2 5-Minute Check 5

8 A. B. C. D. 5-Minute Check 6

9 Mathematical Practices 7 Look for and make use of structure.
Content Standards G.C.2 Identify and describe relationships among inscribed angles, radii, and chords. G.C.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. Mathematical Practices 7 Look for and make use of structure. 3 Construct viable arguments and critique the reasoning of others. CCSS

10 You found measures of interior angles of polygons.
Find measures of inscribed angles. Find measures of angles of inscribed polygons. Then/Now

11 inscribed angle intercepted arc Vocabulary

12 Concept

13 Concept

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

15 Use Inscribed Angles to Find Measures
= 2(52) or 104 Example 1

16 A. Find mC. A. 47 B. 54 C. 94 D. 188 Example 1

17 B. A. 47 B. 64 C. 94 D. 96 Example 1

18 Concept

19 R  S R and S both intercept .
Use Inscribed Angles to Find Measures ALGEBRA Find mR. R  S R and S both intercept mR  mS Definition of congruent angles 12x – 13 = 9x + 2 Substitution x = 5 Simplify. Answer: So, mR = 12(5) – 13 or 47. Example 2

20 ALGEBRA Find mI. A. 4 B. 25 C. 41 D. 49 Example 2

21 Write a two-column proof. Given: Prove: ΔMNP  ΔLOP
Use Inscribed Angles in Proofs Write a two-column proof. Given: Prove: ΔMNP  ΔLOP Proof: Statements Reasons 1. Given LO  MN 2. If minor arcs are congruent, then corresponding chords are congruent. Example 3

22 3. Definition of intercepted arc M intercepts and L intercepts .
Use Inscribed Angles in Proofs Proof: Statements Reasons 3. Definition of intercepted arc M intercepts and L intercepts M  L Inscribed angles of the same arc are congruent. MPN  OPL 5. Vertical angles are congruent. ΔMNP  ΔLOP 6. AAS Congruence Theorem Example 3

23 Write a two-column proof. Given: Prove: ΔABE  ΔDCE
Select the appropriate reason that goes in the blank to complete the proof below. Proof: Statements Reasons 1. Given AB  DC 2. If minor arcs are congruent, then corresponding chords are congruent. Example 3

24 3. Definition of intercepted arc D intercepts and A intercepts .
Proof: Statements Reasons 3. Definition of intercepted arc D intercepts and A intercepts D  A 4. Inscribed angles of the same arc are congruent. DEC  BEA 5. Vertical angles are congruent. ΔDCE  ΔABE 6. ____________________ Example 3

25 A. SSS Congruence Theorem B. AAS Congruence Theorem
C. Definition of congruent triangles D. Definition of congruent arcs Example 3

26 Concept

27 ΔABC is a right triangle because C inscribes a semicircle.
Find Angle Measures in Inscribed Triangles ALGEBRA Find mB. ΔABC is a right triangle because C inscribes a semicircle. mA + mB + mC = 180 Angle Sum Theorem (x + 4) + (8x – 4) + 90 = 180 Substitution 9x + 90 = 180 Simplify. 9x = 90 Subtract 90 from each side. x = 10 Divide each side by 9. Answer: So, mB = 8(10) – 4 or 76. Example 4

28 ALGEBRA Find mD. A. 8 B. 16 C. 22 D. 28 Example 4

29 Concept

30 Find Angle Measures INSIGNIAS An insignia is an emblem that signifies rank, achievement, membership, and so on. The insignia shown is a quadrilateral inscribed in a circle. Find mS and mT. Example 5

31 Answer: So, mS = 90 and mT = 8(8) + 4 or 68.
Find Angle Measures Since TSUV is inscribed in a circle, opposite angles are supplementary. mS + mV = mU + mT = 180 mS = 180 (14x) + (8x + 4) = 180 mS = 90 22x + 4 = 180 22x = 176 x = 8 Answer: So, mS = 90 and mT = 8(8) + 4 or 68. Example 5

32 INSIGNIAS An insignia is an emblem that signifies rank, achievement, membership, and so on. The insignia shown is a quadrilateral inscribed in a circle. Find mN. A. 48 B. 36 C. 32 D. 28 Example 5

33 End of the Lesson


Download ppt "Splash Screen."

Similar presentations


Ads by Google