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 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.

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:

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

Identify congruent parts 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:

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

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

Use properties of congruent figures EXAMPLE 4 Use properties of congruent figures Now you try… In the diagram at the right, ABGH CDEF. Find the value of x and find m H. 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