**Similar** figures *have the same shape*, but *might not be the same size*.

- When two shapes are similar, their corresponding sides are proportional (see ratios and proportions) and their corresponding angles are congruent.
- An older sister and a younger sister might be considered similar

**Congruent **figures *have the same shape *and *size*.

- When two shapes are congruent, their corresponding sides and angles are congruent.
- Identical twins might be considered congruent

**Here are two symbols that you need to know:**

~ means similar

≅ means congruent

*Look Out**: be careful when reading which sides correspond to each other; the shapes may be rotated.*

## Similar Figures Practice:

Quadrilaterals ABCD and EFGH are congruent (ABCD ≅ EFGH). Find the measure of each missing angle and side. | |

The shapes have been rotated, so we need to read the order of the points to find the corresponding angles (ABCD ≅ EFGH). This means that A corresponds to E, B corresponds to F, C corresponds to G, and D corresponds to H. Since the corresponding angles are congruent: | |

This is also true for the corresponding sides: | |

Triangles ABC and DEF are similar (ABC ~ DEF). What is the length of side DF? | |

Here the shapes have not been rotated. A corresponds to D, B corresponds to E, and so on. When the shapes are similar, the ratio of the sides are proportional. Be careful | |

The sun casts a shadow on two trees in a field. The smaller of the two is 10.5 ft high and has a shadow 11.25 ft long. The shadow of the taller tree is 17.5 ft long. How tall is that tree? *This is actually how the heights of many tall structures are estimated!*
| |

When the sun rays hit the trees and cast a shadow it creates proportional triangles. To solve this problem, all we need to do is solve for the missing height. | |

So that tree is a whopping 16 ⅓ feet tall. | |

Pentagons OPQRS and TUVWX are both regular. Find the length of the apothem of TUVWX. *The apothem is the distance from the center of a regular polygon to the midpoint of one side.*
| |

Two regular pentagons are always similar, since all the angles are congruent. Not only are their sides proportional, but their heights and apothems will be proportional too. | |

What are *m* ∠ *K* and *m* of line *MJ*?

Hint

corresponding angles and sides are congruent

Answer

Triangle *RST* ~ Triangle *UVW*. Find the length of sides *ST* and *VU*. Round to the nearest hundredths place.

Hint

side RT corresponds to side UW

Answer

The sun casts a 23 foot shadow on a flagpole. You are 5 feet 3 inches and cast an 11 foot shadow. Approximately how tall is the flagpole? Round to the nearest hundredths place.

Hint

5 ft 3 in is equal to 5.25 ft

Answer

One square has side lengths of 5 cm, and a diagonal ≅ 7.07 cm. Another square has side lengths of 8 cm. What is the length of its diagonal?