Geometry - Loudoun County Public Schools



Name: ____________________________________ Block:________________

Chapter 6

Similarity

Sections Covered:

6.1 Ratios, Proportions, and Geometric Mean

6.2 Proportions in Geometric Problem Solving

6.3 Similar Polygons

6.4 Prove Triangles Similar by AA

6.5 Prove Triangles Similar by SSS and SAS

6.6 Proportionality Theorems

The student, given information in the form of a figure or statement, will prove two triangles are similar, using algebraic and coordinate methods as well as deductive proofs.

Unit 5 Syllabus: Ch. 6 Similarity

|Block |Date |Topic |Homework |

|11 |M 12/8 |6.1 Ratios, Proportions and Geometric Mean |Worksheet 6.2 and 6.3 |

| |T 12/9 |6.2 Use Proportions to Solve Geometry Problems | |

| | |6.3 Use Similar Polygons | |

|12 |W 12/10 |6.4 Prove Triangles Similar by AA |Worksheet 6.4 and 6.5 |

| |Th 12/11 |6.5 Prove Triangles Similar by SSS and SAS | |

|13 |F 12/12 |6.6 Use Proportionality Theorems |Worksheet 6.6 |

| |M 12/15 | | |

|14 |T 12/16 |Ch 6 Review |Worksheet Ch 6 Review |

| |W 12/17 | | |

|15 |Th 12/18 |Ch 6 Quest |Mid-Term Review Packet |

| |F 12/19 | | |

***Syllabus subject to change due to weather, pep rallies, illness, etc

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Ratio of a to b ( [pic] ( a:b

Simplifying Ratios: ( denominators cannot be zero

← must have the same units

← must be simplified

[pic]

6. The area of a rectangle is 108 cm2. 7. If the measures of the angles in a triangle

The ratio of the width to the length is 3:4. have the ratio of 4:5:6, classify the triangle

Find the length and the width. as right, obtuse or acute.

8. In the diagram, [pic]. Find BA and BD.

9. In the diagram, [pic]. Find AC.

The ____________________ of two positive numbers a and b is the positive number x that satisfies:

11. Find the Geometric Mean of:

a. 4 and 9 b. 16 and 18 c. 6 and 20 d. 8 is the geometric mean of 4 and what number?

Notes: 6.2 Use Proportions to Solve Geometry Problems

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Proportion: equation that equates two ratios [pic]

Properties:

a. Cross Products b. Reciprocal

[pic]

c. If [pic], then [pic]. d. If [pic], then [pic].

Practice: Complete each statement.

1. If [pic] 2. If [pic]

3. If [pic] 4. If [pic]

Decide whether the statement is True or False.

5. If [pic] 6. If [pic] 7. If [pic]

8. If [pic] 9. If [pic]

Solve for x.

[pic]

Solve for the variable.

13. MN:MO is 3:4 14. (PQR side lengths: (STU side lengths is 1:3

Use the diagram and the given information to find the unknown length.

15. Given [pic] 16. Given [pic]

.

Notes: 6.3 Use Similar Polygons

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Similar Polygons: SYMBOL for SIMILAR: ________

Corresponding angles are _____________________________________________

Corresponding sides are _______________________________________________

Writing Similarity Statements:

Corresponding ................
................

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