Congruent Figures Locust Grove Middle School Academy 8

Congruent Figures Locust Grove Middle School Academy 8 th Grade Math

Congruent Figures If one shape can become another using turns, flips and or slides, then the shapes are CONGRUENT. Rotation (Turn) Reflection (Flip) Translation (Slide) After any of these turns, flips, or slides (transformations) the shape still has the same size, area, angles, and measurements.

This symbol means Congruent Star 2 Star 1 is congruent to Star 2

H N ΔMHS ≅ ΔONE M S O THIS IS NOT THE SAME AS ΔMHS ≅ ΔNEO E

The two triangles are congruent. Find the missing side length and angle measures W W 6. 6 ft R Z X 5. 2 ft 45° Y 4. 5 ft Triangle has 180°… First, what do we 180° - 90° - 45° = 45° X = 90° know? Y = 45° S If the shapes are congruent, their area, angles, size and side lengths are equal Then, we can determine… W = 45° Z = 5. 2 ft R = 6. 6 ft S = 4. 5 ft

Remember Two shapes need to be the SAME SIZE to be congruent.

Similar Figures You can use indirect measurement to find the length, When you need to resize one shape to make it the same width or height of objects that are too difficult to measure as the other, the shapes are called SIMILAR. directly.

Example of Similar Figures Triangle A You can multiply Triangle A’s sides by ½ and get the length of Triangle B’s sides Triangle B AND You can multiply Triangle B’s sides by 2 and get the length of Triangle A’s sides

Find the missing side 30 X 10 5 How do we do this? 10 30 Set up a. Cross ratio multiply… 150 = 10 X 5 = X Divide by 10… X = 15

Are these figures similar? 16 4 6 2 First set up your ratio. 2 4 = 6 16 Then if we cross multiply…. we get 32 = 24 This is not true, 32 DOES NOT EQUAL 24. Therefore the figures ARE NOT similar!

If you only…. Then the shapes are… Flip, Turn, and/or Slide (Rotate, Reflect, and/or Translate) CONGRUENT SIMILAR Need to resize Congruent Similar

Any Questions?