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Transformations Practice Study Triangle RST was dilated by a scale factor of. The image, triangle R'S'T', is an isosceles triangle, with each leg measuring 8 units. What is the length of a leg of the pre-image, triangle RST? 16 units Why is the information in the diagram enough to determine that △LMN ~ △PON using a rotation about point N and a dilation? because one pair of congruent corresponding angles is sufficient to determine similar triangles Quadrilateral JKLM was dilated according to the rule DO,(x,y) - > (1/2x, 1/2y)0, - 4) to create the image quadrilateral J'K'L'M', which is shown on the graph. What are the coordinates of vertex J of the pre-image? (0, - 4) Triangle ABC was dilated using the rule DY, 5/4. If CA = 8, what is C'A'? 10 units Which statements can be concluded from the diagram and used to prove that the triangles are similar by the SAS similarity theorem? A Read the proof. Given: AB ∥ DE Prove: △ACB ~ △DCE
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We are given AB ∥ DE. Because the lines are parallel and segment CB crosses both lines, we can consider segment CB a transversal of the parallel lines. Angles CED and CBA are corresponding angles of transversal CB and are therefore congruent, so ∠CED ≅ ∠CBA. We can state ∠C ≅ ∠C using the reflexive property. Therefore, △ACB ~ △DCE by the AA similarity theorem. Consider the two triangles. To prove that the triangles are similar by the SSS similarity theorem, it needs to be shown that AB = 25 and HG = 15 Triangle TVW is dilated according to the rule DO 3/4,(x,y) - > (3/4x 3/4y) to create the image triangle T'V'W', which is not shown. What are the coordinates of the endpoints of the segment T'V'? T'(-3, 6) and V'(0, 3) Which best explains why all equilateral triangles are similar? All equilateral triangles can be mapped onto each other using dilations. Is rectangle EFGH the result of a dilation of rectangle ABCD with a center of dilation at the origin? Why or why not? Yes, because both figures are rectangles and all rectangles are similar. Consider △RST and △RYX. If the triangles are similar, which must be true? B If an image of a triangle is congruent to the pre-image, then the scale factor of the dilation must be n = 1 Parallelogram FGHJ was dilated and translated to form similar parallelogram F'G'H'J'.
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Triangle MNO was dilated, then ____________, to create triangle YHQ. rotated Triangle MNP will be dilated according to the rule (x,y), where point P is the center of dilation. What will be the coordinates of vertex N' of the image? (-2, 6) In the diagram below, m∠A = 55° and m∠E = 35°. Which best explains the relationship between triangle ACB and triangle DCE? The triangles are similar because all pairs of corresponding angles are congruent. Triangle JKL was dilated using the rule DM, 1/3. The image, triangle J'K'L', is the result of the dilation. What is L'L? 5 units
