wednesday, april 26, 2017 warm up
DESCRIPTION
Properties of Tangents Wednesday, April 26, 2017 Essential Question: How do we use properties of a tangent to a circle? Lesson 6.1TRANSCRIPT
![Page 1: Wednesday, April 26, 2017 Warm Up](https://reader035.vdocuments.net/reader035/viewer/2022062503/5a4d1aed7f8b9ab05997c1a3/html5/thumbnails/1.jpg)
MM2G3 Students will understand properties of circles.
MM2G3 a Understand and use properties of chords, tangents, and secants as an application of triangle similarity.
Warm UpWednesday, May 3, 2023
1. What is the length of the diagonal of a square with side lengths ?7 2
2. In a 45o45o90o triangle, what is the length of each leg if the hypotenuse is 8?
xy
2260o
3. Find the value of x and y.
4. In a 30o60o90o triangle, the shorter leg is 3.3 feet long. Find the perimeter.
5. Solve: 4x2 + 20 = 0
14
4 2
11, 11 3x y
9.9 3.3 3 feetP
5x i
![Page 2: Wednesday, April 26, 2017 Warm Up](https://reader035.vdocuments.net/reader035/viewer/2022062503/5a4d1aed7f8b9ab05997c1a3/html5/thumbnails/2.jpg)
MM2G3 Students will understand properties of circles.
MM2G3 a Understand and use properties of chords, tangents, and secants as an application of triangle similarity.
Properties of Tangents
Essential Question:How do we use properties of a tangent to a circle?
Wednesday, May 3, 2023
Lesson 6.1
![Page 3: Wednesday, April 26, 2017 Warm Up](https://reader035.vdocuments.net/reader035/viewer/2022062503/5a4d1aed7f8b9ab05997c1a3/html5/thumbnails/3.jpg)
MM2G3 Students will understand properties of circles.
MM2G3 a Understand and use properties of chords, tangents, and secants as an application of triangle similarity.
Daily Homework Quiz
1. Give the name that best describes the figure .
a. CD b. AB
c. FD d. EP
Chord
secant
radius
tangent
![Page 4: Wednesday, April 26, 2017 Warm Up](https://reader035.vdocuments.net/reader035/viewer/2022062503/5a4d1aed7f8b9ab05997c1a3/html5/thumbnails/4.jpg)
MM2G3 Students will understand properties of circles.
MM2G3 a Understand and use properties of chords, tangents, and secants as an application of triangle similarity.
2. Tell how many common tangents the circles have .
ANSWER
One tangent; it is a vertical line through the point of tangency.
Daily Homework Quiz
![Page 5: Wednesday, April 26, 2017 Warm Up](https://reader035.vdocuments.net/reader035/viewer/2022062503/5a4d1aed7f8b9ab05997c1a3/html5/thumbnails/5.jpg)
MM2G3 Students will understand properties of circles.
MM2G3 a Understand and use properties of chords, tangents, and secants as an application of triangle similarity.
Perpendicular Tangent Theorem 6.1
In a plane, if a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency.
If l is tangent to Q at P, then l QP.
l
Q
P
![Page 6: Wednesday, April 26, 2017 Warm Up](https://reader035.vdocuments.net/reader035/viewer/2022062503/5a4d1aed7f8b9ab05997c1a3/html5/thumbnails/6.jpg)
MM2G3 Students will understand properties of circles.
MM2G3 a Understand and use properties of chords, tangents, and secants as an application of triangle similarity.
Tangent Theorems
Create right triangles for problem solving.
![Page 7: Wednesday, April 26, 2017 Warm Up](https://reader035.vdocuments.net/reader035/viewer/2022062503/5a4d1aed7f8b9ab05997c1a3/html5/thumbnails/7.jpg)
MM2G3 Students will understand properties of circles.
MM2G3 a Understand and use properties of chords, tangents, and secants as an application of triangle similarity.
1. Find the segment length indicated. Assume that lines which appear tangent are tangent.
![Page 8: Wednesday, April 26, 2017 Warm Up](https://reader035.vdocuments.net/reader035/viewer/2022062503/5a4d1aed7f8b9ab05997c1a3/html5/thumbnails/8.jpg)
MM2G3 Students will understand properties of circles.
MM2G3 a Understand and use properties of chords, tangents, and secants as an application of triangle similarity.
2. Find the segment length indicated. Assume that lines which appear tangent are tangent.
![Page 9: Wednesday, April 26, 2017 Warm Up](https://reader035.vdocuments.net/reader035/viewer/2022062503/5a4d1aed7f8b9ab05997c1a3/html5/thumbnails/9.jpg)
MM2G3 Students will understand properties of circles.
MM2G3 a Understand and use properties of chords, tangents, and secants as an application of triangle similarity.
3. Find the segment length indicated. Assume that lines which appear tangent are tangent.
![Page 10: Wednesday, April 26, 2017 Warm Up](https://reader035.vdocuments.net/reader035/viewer/2022062503/5a4d1aed7f8b9ab05997c1a3/html5/thumbnails/10.jpg)
MM2G3 Students will understand properties of circles.
MM2G3 a Understand and use properties of chords, tangents, and secants as an application of triangle similarity.
4. Find the segment length indicated. Assume that lines which appear tangent are tangent.
![Page 11: Wednesday, April 26, 2017 Warm Up](https://reader035.vdocuments.net/reader035/viewer/2022062503/5a4d1aed7f8b9ab05997c1a3/html5/thumbnails/11.jpg)
MM2G3 Students will understand properties of circles.
MM2G3 a Understand and use properties of chords, tangents, and secants as an application of triangle similarity.
5. Find the segment length indicated. Assume that lines which appear tangent are tangent.
![Page 12: Wednesday, April 26, 2017 Warm Up](https://reader035.vdocuments.net/reader035/viewer/2022062503/5a4d1aed7f8b9ab05997c1a3/html5/thumbnails/12.jpg)
MM2G3 Students will understand properties of circles.
MM2G3 a Understand and use properties of chords, tangents, and secants as an application of triangle similarity.
Find the radius of a circle
6. In the diagram, ʘB is a point of tangency. Find the radius r of ʘC.
SOLUTION
You know that AB BC , so △ ABC is a right triangle. You can use the Pythagorean Theorem.
AC2 = BC2 + AB2
(r + 50)2 = r2 + 802
r2 + 100r + 2500 = r2 + 6400100r = 3900
r = 39 ft .
Pythagorean Theorem
Substitute.Write the binomial twice.
Subtract from each side.Divide each side by 100.
(r + 50)(r + 50) = r2 + 802
r2 + 50r +50r + 2500 = r2 + 6400Combine Like Terms.Multiply.
![Page 13: Wednesday, April 26, 2017 Warm Up](https://reader035.vdocuments.net/reader035/viewer/2022062503/5a4d1aed7f8b9ab05997c1a3/html5/thumbnails/13.jpg)
MM2G3 Students will understand properties of circles.
MM2G3 a Understand and use properties of chords, tangents, and secants as an application of triangle similarity.
7. ST is tangent to ʘ Q. Find the value of r.
SOLUTION
You know from Theorem 10.1 that ST QS , so △ QST is a right triangle. You can use the Pythagorean Theorem.
r2 + 36r + 324 = r2 + 576
36r = 252
r = 7
Multiply.
Subtract from each side.
Divide each side by 36.
QT2 = QS2 + ST2
(r + 18)2 = r2 + 242
Pythagorean Theorem
Substitute.
Find the radius of a circle
![Page 14: Wednesday, April 26, 2017 Warm Up](https://reader035.vdocuments.net/reader035/viewer/2022062503/5a4d1aed7f8b9ab05997c1a3/html5/thumbnails/14.jpg)
MM2G3 Students will understand properties of circles.
MM2G3 a Understand and use properties of chords, tangents, and secants as an application of triangle similarity.
Perpendicular Tangent Converse
In a plane, if a line is perpendicular to a radius of a circle at its endpoint on the circle, then the line is tangent to the circle.
l
Q
P
If l QP at P, then l is tangent to Q.
![Page 15: Wednesday, April 26, 2017 Warm Up](https://reader035.vdocuments.net/reader035/viewer/2022062503/5a4d1aed7f8b9ab05997c1a3/html5/thumbnails/15.jpg)
MM2G3 Students will understand properties of circles.
MM2G3 a Understand and use properties of chords, tangents, and secants as an application of triangle similarity.
8. Determine if line AB is tangent to the circle.
Verify a tangent to a circle
![Page 16: Wednesday, April 26, 2017 Warm Up](https://reader035.vdocuments.net/reader035/viewer/2022062503/5a4d1aed7f8b9ab05997c1a3/html5/thumbnails/16.jpg)
MM2G3 Students will understand properties of circles.
MM2G3 a Understand and use properties of chords, tangents, and secants as an application of triangle similarity.
9. Determine if line AB is tangent to the circle. Verify a tangent to a circle
![Page 17: Wednesday, April 26, 2017 Warm Up](https://reader035.vdocuments.net/reader035/viewer/2022062503/5a4d1aed7f8b9ab05997c1a3/html5/thumbnails/17.jpg)
MM2G3 Students will understand properties of circles.
MM2G3 a Understand and use properties of chords, tangents, and secants as an application of triangle similarity.
GUIDED PRACTICE
10. Is DE tangent to ʘ C?
ANSWER
Yes – The length of CE is 5 because the radius is 3 and the outside portion is 2. That makes ∆CDE a 3-4-5 Right Triangle. So DE and CD are
Verify a tangent to a circle
![Page 18: Wednesday, April 26, 2017 Warm Up](https://reader035.vdocuments.net/reader035/viewer/2022062503/5a4d1aed7f8b9ab05997c1a3/html5/thumbnails/18.jpg)
MM2G3 Students will understand properties of circles.
MM2G3 a Understand and use properties of chords, tangents, and secants as an application of triangle similarity.
Verify a tangent to a circle
SOLUTION
Use the Converse of the Pythagorean Theorem. Because 122 + 352 = 372, △ PST is a right triangle and ST PT . So, ST is perpendicular to a radius of ʘ P at its endpoint on ʘ P. ST is tangent to ʘ P.
11. In the diagram, PT is a radius of ʘ P. Is ST tangent to ʘ P ?
![Page 19: Wednesday, April 26, 2017 Warm Up](https://reader035.vdocuments.net/reader035/viewer/2022062503/5a4d1aed7f8b9ab05997c1a3/html5/thumbnails/19.jpg)
MM2G3 Students will understand properties of circles.
MM2G3 a Understand and use properties of chords, tangents, and secants as an application of triangle similarity.
HomeworkPage 186 # 12 – 17.Page 188 # 17 – 19.