Splash Screen

Lesson Menu Five-Minute Check (over Lesson 4–6) CCSS Then/Now New Vocabulary Key Concept: Reflections, Translations, and Rotations Example 1:Identify Congruence Transformations Example 2:Real-World Example: Identify a Real-World Transformation Example 3:Verify Congruence after a Transformation

Over Lesson 4–6 5-Minute Check 1 Name two congruent segments if  1   2. A. B. C. D.

Over Lesson 4–6 5-Minute Check 2 A.  R   W B.  S   V C.  S   U D.  S   T

Over Lesson 4–6 5-Minute Check 3 A.30 B.40 C.50 D.60 Find m  R if m  RUV = 65.

Over Lesson 4–6 5-Minute Check 4 A.45 B.55 C.70 D.110 Find m  C if ΔABC is isosceles with AB  AC and m  A = 70. ___

Over Lesson 4–6 5-Minute Check 5 A.20 B.10 C.5 D.2 Find x if ΔLMN is equilateral with LM = 2x – 4, MN = x + 6, and LN = 3x – 14.

Over Lesson 4–6 5-Minute Check 6 In isosceles triangle BCD,  C is the vertex angle. Which sides are congruent? A.BC  CD B.BC  BD C.BD  CD D.no sides are congruent

CCSS Content Standards G.CO.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. G.CO.7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. Mathematical Practices 1 Make sense of problems and persevere in solving them. 7 Look for and make use of structure.

Then/Now You proved whether two triangles were congruent. Identify reflections, translations, and rotations. Verify congruence after a congruence transformation.

Vocabulary transformation preimage image congruence transformation isometry reflection translation rotation

Concept

Example 1 Identify Congruence Transformations A. Identify the type of congruence transformation shown as a reflection, translation, or rotation. Each vertex and its image are in the same position, just 5 units right and 2 units down. Answer: This is a translation.

Example 1 Identify Congruence Transformations B. Identify the type of congruence transformation shown as a reflection, translation, or rotation. Each vertex and its image are the same distance from the origin. The angles formed by each pair of corresponding points and the origin are congruent. Answer: This is a rotation.

Example 1 Identify Congruence Transformations C. Identify the type of congruence transformation shown as a reflection, translation, or rotation. Each vertex and its image are the same distance from the x-axis. Answer: This is a reflection.

Example 1A A.reflection B.translation C.rotation D.none of these A. Identify the type of congruence transformation shown as a reflection, translation, or rotation.

Example 1B A.reflection B.translation C.rotation D.none of these B. Identify the type of congruence transformation shown as a reflection, translation, or rotation.

Example 1C A.reflection B.translation C.rotation D.none of these C. Identify the type of congruence transformation shown as a reflection, translation, or rotation.

Example 2 Identify a Real-World Transformation BRIDGES Identify the type of congruence transformation shown by the image of the bridge in the river as a reflection, translation, or rotation. Answer: The image is a reflection, with the line at which the bridge meets the water as the line of reflection.

Example 2 A.reflection B.translation C.rotation D.none of these GAME Identify the type of congruence transformation shown by the image of the chess piece as a reflection, translation, or rotation.

Example 3 Verify Congruence after a Transformation Triangle PQR with vertices P(4, 2), Q(3, –3), and R(5, –2) is a transformation of ΔJKL with vertices J(–2, 0), K(–3, –5), and L(–1, –4). Graph the original figure and its image. Identify the transformation and verify that it is a congruence transformation. UnderstandYou are asked to identify the type of transformation—reflection, translation, or rotation. Then, you need to show that the two figures are congruent. Plan Use the Distance Formula to find the measure of each side. Then show that the two triangles are congruent by SSS.

Example 3 Verify Congruence after a Transformation SolveGraph each figure. The transformation appears to be a translation 6 units right and 2 units up. Find the measures of the sides of each triangle.

Example 3 Verify Congruence after a Transformation

Example 3 Verify Congruence after a Transformation Answer:By SSS, ΔJKL  ΔPQR. CheckUse the definition of a translation. Use a ruler to measure and compare the corresponding sides of the triangles. The corresponding sides are congruent, so the triangles are congruent.

Example 3 Triangle ABC with vertices A(–1, –4), B(–4, –1), and C(–1, –1) is a transformation of ΔXYZ with vertices X(–1, 4), Y(–4, 1), and Z(–1, 1). Graph the original figure and its image. Identify the transformation and verify that it is a congruence transformation. A. B. C. D.

End of the Lesson