1 / 14

Understanding Congruent Figures: Optical Illusions and Real-World Examples

Explore how to identify congruent figures through optical illusions and real-world examples. Learn about shapes, sizes, and more in this informative guide.

claudettea
Télécharger la présentation

Understanding Congruent Figures: Optical Illusions and Real-World Examples

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Which center circle do you think is bigger? In spite of appearances, the two center circles are congruent. Their apparent differences are optical illusions. One way to determine whether figures are congruent is to see if one figure will fit exactly over the other one. Look at the two patterns.

  2. Additional Example 1: Identifying Congruent Figures in the Real World Identify any congruent figures. A. The sides of the octagons are not congruent. Each side of the outer figure is larger than each side of the inner figure.

  3. Additional Example 1: Identifying Congruent Figures in the Real World Identify any congruent figures. B. The sectors in the figure are congruent.

  4. Remember! Two figures are congruent if they have the same shape and size.

  5. Check It Out! Example 1 Identify any congruent figures. A. The sides of the figures are are not congruent.

  6. Check It Out! Example 1 Identify any congruent figures. B. The figures are not congruent. The figure on the outside is larger than the one on the inside.

  7. If all of the corresponding sides and angles of two polygons are congruent, then the polygons are congruent.

  8. Additional Example 2: Identifying Congruent Triangles Determine whether the triangles are congruent. Q C 4 cm 4 cm AB = 4 cm BC = 4 cm AC = 6 cm PQ = 4 cm PR = 4 cm RQ = 5 cm B P 5 cm 6 cm 4 cm 4 cm R A The triangles are not congruent. Although two sides in one triangle are congruent to two sides in the other, the third sides are not congruent.

  9. Check It Out! Example 2 Determine whether the triangles are congruent. B E AC = 8 m AB = 6 m BC = 10 m DF = 8 m DE = 6 m EF = 10 m 10 m 10 m 6 m 6 m A C D F 8 m 8 m

  10. For polygons with more than three sides, it is not enough to compare the measures of their sides. For example, the corresponding sides of the figures below are congruent, but the figures are not congruent. If you know that two figures are congruent, you can find the missing measures in the figures.

  11. Additional Example 3: Using Congruence to Find Missing Measures Determine the missing measure in the set of congruent polygons. A. The corresponding angles of congruent polygons are congruent. The missing angle measure is 110°.

  12. Additional Example 3: Using Congruence to Find Missing Measures Determine the missing measure in the set of congruent polygons. B. The corresponding sides of congruent polygons are congruent. The missing side length is 28 mm.

  13. Check It Out! Example 3 Determine the missing measure in the set of congruent polygons. A. ? 135° 120° 5 ft 6 ft The corresponding sides are congruent. 45° 60° 8 ft The missing side length is 4 ft. 8 ft 60° 45° 6 ft 5 ft 135° 120° 4 ft

  14. Check It Out! Example 3 Determine the missing measure in the set of congruent polygons. B. 6 ft 130° 110° 5 ft The corresponding angles are congruent. 8 ft 120° 80° 4 ft 100° 10 ft The missing angle measure is 130°. 10 ft 100° 80° 4 ft 120° 8 ft ? 110° 5 ft 6 ft

More Related