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Lesson Menu Five-Minute Check (over Lesson 10–4) CCSS Then/Now New Vocabulary Example 1:Identify Common Tangents Theorem Example 2:Identify a Tangent Example 3:Use a Tangent to Find Missing Values Theorem Example 4:Use Congruent Tangents to Find Measures Example 5:Real-World Example: Find Measures in Circimscribed Polygons

Over Lesson 10–4 5-Minute Check 1 A.60 B.55 C.50 D.45 Refer to the figure. Find m  1.

Over Lesson 10–4 5-Minute Check 1 A.60 B.55 C.50 D.45 Refer to the figure. Find m  1.

Over Lesson 10–4 5-Minute Check 2 A.30 B.25 C.20 D.15 Refer to the figure. Find m  2.

Over Lesson 10–4 5-Minute Check 2 A.30 B.25 C.20 D.15 Refer to the figure. Find m  2.

Over Lesson 10–4 5-Minute Check 3 A.35 B.30 C.25 D.20 Refer to the figure. Find m  3.

Over Lesson 10–4 5-Minute Check 3 A.35 B.30 C.25 D.20 Refer to the figure. Find m  3.

Over Lesson 10–4 5-Minute Check 4 A.120 B.100 C.80 D.60 Refer to the figure. Find m  4.

Over Lesson 10–4 5-Minute Check 4 A.120 B.100 C.80 D.60 Refer to the figure. Find m  4.

Over Lesson 10–4 5-Minute Check 5 A.10 B.11 C.12 D.13 find x if m  A = 3x + 9 and m  B = 8x – 4.

Over Lesson 10–4 5-Minute Check 5 A.10 B.11 C.12 D.13 find x if m  A = 3x + 9 and m  B = 8x – 4.

Over Lesson 10–4 5-Minute Check 6 A.47.5° B.95° C.190° D.265° The measure of an arc is 95°. What is the measure of an inscribed angle that intercepts it?

Over Lesson 10–4 5-Minute Check 6 A.47.5° B.95° C.190° D.265° The measure of an arc is 95°. What is the measure of an inscribed angle that intercepts it?

CCSS Content Standards G.CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). G.C.4 Construct a tangent line from a point outside a given circle to the circle. Mathematical Practices 1 Make sense of problems and persevere in solving them. 2 Reason abstractly and quantitatively.

Then/Now You used the Pythagorean Theorem to find side lengths of right triangles. Use properties of tangents. Solve problems involving circumscribed polygons.

Vocabulary tangent point of tangency common tangent

Example 1 Identify Common Tangents A. Copy the figure and draw the common tangents. If no common tangent exists, state no common tangent. Answer:

Example 1 Identify Common Tangents A. Copy the figure and draw the common tangents. If no common tangent exists, state no common tangent. Answer: These circles have no common tangents. Any tangent of the inner circle will intercept the outer circle in two points.

Example 1 Identify Common Tangents B. Copy the figure and draw the common tangents. If no common tangent exists, state no common tangent. Answer:

Example 1 Identify Common Tangents B. Copy the figure and draw the common tangents. If no common tangent exists, state no common tangent. Answer: These circles have 2 common tangents.

Example 1 A.2 common tangents B.4 common tangents C.6 common tangents D.no common tangents A. Copy the figure and draw the common tangents to determine how many there are. If no common tangent exists, choose no common tangent.

Example 1 A.2 common tangents B.4 common tangents C.6 common tangents D.no common tangents A. Copy the figure and draw the common tangents to determine how many there are. If no common tangent exists, choose no common tangent.

Example 1 A.2 common tangents B.3 common tangents C.4 common tangents D.no common tangents B. Copy the figure and draw the common tangents to determine how many there are. If no common tangent exists, choose no common tangent.

Example 1 A.2 common tangents B.3 common tangents C.4 common tangents D.no common tangents B. Copy the figure and draw the common tangents to determine how many there are. If no common tangent exists, choose no common tangent.

Concept

Example 2 Identify a Tangent Test to see if ΔKLM is a right triangle. ? = 29 2 Pythagorean Theorem 841 =841 Simplify. Answer:

Example 2 Identify a Tangent Test to see if ΔKLM is a right triangle. ? = 29 2 Pythagorean Theorem 841 =841 Simplify. Answer:

Example 2 A. B.

Example 2 A. B.

Example 3 Use a Tangent to Find Missing Values EW 2 + DW 2 =DE 2 Pythagorean Theorem x 2 =(x + 16) 2 EW = 24, DW = x, and DE = x x 2 =x x + 256Multiply. 320 =32xSimplify. 10 =xDivide each side by 32. Answer:

Example 3 Use a Tangent to Find Missing Values EW 2 + DW 2 =DE 2 Pythagorean Theorem x 2 =(x + 16) 2 EW = 24, DW = x, and DE = x x 2 =x x + 256Multiply. 320 =32xSimplify. 10 =xDivide each side by 32. Answer: x = 10

Example 3 A.6 B.8 C.10 D.12

Example 3 A.6 B.8 C.10 D.12

Concept

Example 4 Use Congruent Tangents to Find Measures AC =BCTangents from the same exterior point are congruent. 3x + 2 =4x – 3Substitution 2 =x – 3Subtract 3x from each side. 5 =xAdd 3 to each side. Answer:

Example 4 Use Congruent Tangents to Find Measures AC =BCTangents from the same exterior point are congruent. 3x + 2 =4x – 3Substitution 2 =x – 3Subtract 3x from each side. 5 =xAdd 3 to each side. Answer: x = 5

Example 4 A.5 B.6 C.7 D.8

Example 4 A.5 B.6 C.7 D.8

Example 5 Find Measures in Circumscribed Polygons Step 1Find the missing measures.

Example 5 Find Measures in Circumscribed Polygons Step 2Find the perimeter of ΔQRS. Answer: = or 36 cm

Example 5 Find Measures in Circumscribed Polygons Step 2Find the perimeter of ΔQRS. Answer: So, the perimeter of ΔQRS is 36 cm. = or 36 cm

Example 5 A.42 cm B.44 cm C.48 cm D.56 cm

Example 5 A.42 cm B.44 cm C.48 cm D.56 cm

End of the Lesson