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Geometry A Bellwork Sheet # 7

This worksheet covers the concept of congruent figures in geometry, specifically focusing on trapezoids and triangles. Congruent figures are defined as having the same size and shape, with corresponding angles and sides being congruent. Example problems include finding variables in quadrilaterals through algebraic equations, as well as applications of the Third-Angle Theorem to deduce congruence between triangles. Students will practice identifying corresponding parts in congruent figures and solving for unknown variable values in geometric contexts.

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Geometry A Bellwork Sheet # 7

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  1. Geometry A Bellwork Sheet # 7 52° 1) Find the value of the variable. (2x)°

  2. 4-1 Congruent Figures

  3. Congruent Figures • Congruent figures have the same size and shape. • They have corresponding sides that are congruent. • They have corresponding angles that are congruent. These trapezoids are congruent.

  4. EX. ∆EFG is congruent to ∆FGH Name all corresponding parts. E H G F ANGLES SIDES E H EF HF F F EG HG G G GF GF

  5. IH RS 3a = 6 3a = 6 3 3 In the figure, quadrilateral JIHK quadrilateral QRST. Find a. Divide both sides by 3. 3a I H a = 2 6 4b° S R 120° J 30° Q K c + 10° T

  6. H S 4b = 120 4b = 120 4 4 In the figure, quadrilateral JIHK quadrilateral QRST. Find b. Divide both sides by 4. 3a I H 6 4b° S R b = 30° 120° J 30° Q K c + 10° T

  7. K T c + 10 = 30 c + 10 = 30 –10 –10 In the figure, quadrilateral JIHK quadrilateral QRST. Find c. Subtract 10 from both sides. 3a I H 6 c = 20° 4b° S R 120° J 30° Q K c + 10° T

  8. Third-Angle Theorem If two angles of one triangle are congruent to two angles of another triangle, then there third angles are congruent. D A C B E F C = ˜ F

  9. EX. Can you conclude the figures are congruent? Justify your answer. 6 6

  10. OYO. Can you conclude the figures are congruent? Justify your answer. 11 11

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