Congruence “Same size, same shape” Which transformations have we learned that result in congruent figures? ≅ means congruent

Geometric figures are congruent if they are the same size and shape. Corresponding angles and corresponding sides are in the same position in polygons with an equal number of sides. Two polygons are congruent polygons if their corresponding parts are congruent.

What’s congruent?

What’s congruent?

To name a polygon, write the vertices in consecutive order To name a polygon, write the vertices in consecutive order. For example, you can name polygon PQRS as QRSP or SRQP, but not as PRQS.

When you write a statement such as ABC  DEF, you are also stating which parts are congruent. Helpful Hint

Example 1: Given: ∆PQR  ∆STW Identify all pairs of corresponding congruent parts. Angles: P  S, Q  T, R  W Sides: PQ  ST, QR  TW, PR  SW

Example 2: Given: ∆ABC  ∆DBC. Find the value of x.

Example 2: Given: ∆ABC  ∆DEF. Find the value of each: m W = X = m Y = m Z = A (5x+12 )⁰ 60⁰ F Z (2x+24)⁰ Y C B D

Example 4: A(1, 1), B(3, 1), & C(3, 5) are rotated 180ᴼ CW about the origin to create D(–3, –1), E(–1, –1), & F(–3, –5). Name the parts of the triangle that are congruent.

Lesson Quiz ∆ABC  ∆JKL and AB = 2x + 12. JK = 4x – 50. Find x and AB. Given that polygon MNOP  polygon QRST, identify the congruent corresponding part. NO  ____ 3. T  ____ 4. Which transformation does not result in congruent figures? 31, 74 RS P Dilation

Homework!