The following multiple-select question, explained here in hopes of helping geometry students in Maryland and Illinois prepare for the PARCC test near the end of this school year, appears on the released version of PARCC’s Spring 2015 test in geometry, here:
ΔABC is dilated from center A by a factor not equal to 1 to form ΔAKL. Which of the statements must be true?
Select all that apply.
Resources for further study
Math Is Fun, maintained by Rod Pierce, has a nice page that explains the difference between similar and congruent figures. This is elementary stuff, but just as a refresher, check it out, and think about how it applies to doing dilations.
The Khan Academy, developed by Sal Khan, an engineer who has created a library of thousands of video lessons, has more than 20 lesson videos about transforming geometric figures, including expanding and shrinking them by dilating from a certain point. The landing page for the lessons is here.
Chapter 8, Section 8.2, of the book Geometry for Enjoyment and Challenge by Richard Rhoad et al, all teachers from Illinois, deals with similarity in polygons. Similar polygons, they write, are those in which
- The ratios of the measures of corresponding sides are equal
- Corresponding angles are congruent
(Richard Rhoad, George Milauskas, and Robert Whipple. Geometry for Enjoyment and Challenge, new edition. Evanston, Ill.: McDougal Littell, a division of Houghton Mifflin Company, 1991. The book is used in several geometry classes taught in Illinois high schools.)
Analysis of this question and online accessibility
The question measures knowledge of the Common Core standard it purports to measure and tests students’ ability apply the principles of dilations to work with triangle similarity theorems. It is considered to have a low cognitive demand.
The question can be tested online and should yield results that are as valid and reliable as those obtained on paper.
No special accommodation challenges can be identified with this question, so the question is considered fair.
A building casts a 98-foot shadow at the same time that a 29-foot flagpole casts as 31.5-foot shadow. About how tall is the building?
Purpose of this series of posts
Voxitatis is developing blog posts that address every algebra 1 question released to the public by the Partnership for Assessment of Readiness for College and Careers, or PARCC, in order to help students prepare to take the test this spring.
Our total release will run from February 27 through March 15, with one or two questions discussed per day. Then we’ll move to geometry at the end of March, algebra 2 during the first half of April, and eighth grade during the last half of April.