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4.2 – Congruent Figures

4.2 – Congruent Figures. Geometry Ms. Rinaldi. Congruent Figures. Two geometric figures are congruent if they have exactly the same size and shape. Congruent Not Congruent Same size and shape Different sizes or shapes. Congruent Figures.

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4.2 – Congruent Figures

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  1. 4.2 – Congruent Figures Geometry Ms. Rinaldi

  2. Congruent Figures Two geometric figures are congruent if they have exactly the same size and shape. Congruent Not Congruent Same size and shape Different sizes or shapes

  3. Congruent Figures In two congruent figures, all the parts of one figure are congruent to the corresponding parts of the other figure. In congruent polygons, this means that the corresponding sides and the corresponding angles are congruent.

  4. Congruence Statements When you write a congruence statement for two polygons, always list the corresponding vertices in the same order. You can write congruence statements in more than one way. Two possible congruence statements for the triangles are: Now you try…Write a different congruence statement for the triangles:

  5. Write a congruence statement for the triangles. Identify all pairs of congruent corresponding parts. The diagram indicates that JKL TSR. Corresponding angles J T,∠ K S,L R Corresponding sides JK TS,KL SR,LJ RT EXAMPLE 1 Identify congruent parts SOLUTION

  6. EXAMPLE 2 Identify congruent parts Now you try… Write a congruence statement for the triangles. Identify all pairs of congruent corresponding parts. Congruence Statement: Corresponding Angles: Corresponding Sides:

  7. In the diagram, DEFG SPQR. Find the value of x. Find the value of y. You know that FG QR. FG = QR = 2x – 4 12 16 = 2x 8 = x EXAMPLE 3 Use properties of congruent figures SOLUTION

  8. You know that∠ F Q. m F = mQ 68 = 6y + 8 68 o = (6y + x) o 10 = y EXAMPLE 3 Use properties of congruent figures (continued)

  9. In the diagram at the right, ABGH CDEF. Find the value ofxand findm H. Use properties of congruent figures EXAMPLE 4 Now you try… Step 1: Which angle corresponds with angle H? Step 2: You then know that 4x + 5 =_______ Step 3: Solve for x. x = _____ Step 4: Plug in x to find

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