Warm-Up/Opening Activity Use the to determine what students already know. Feel free to add/delete/change statements as they fit your class. Accept students' answers and justifications and ask if the class thinks they are reasonable.

1. Similarity Congruence Worksheets With Answers
2. Congruence And Similarity Pdf
3. Unit 1 Transformations Congruence And Similarity Study Guide Answers

Development of Ideas Worksheet: Ask students to work in groups of 2 or 3 to measure all of the segments listed using a ruler. It is helpful if all students measure using the same unit (suggest measuring in centimeters). It may be helpful to have the students change their ratios to a decimal (about 1.4) to show that the ratios are equal. Explorations/Investigations Present the concept and discover the SSS and SAS postulates of congruency and the SSS, SAS and AA postulates of similarity. Activity One Worksheet: Organize students into groups of two. Each student needs to cut out the three strips of paper.

Place the strips together corner-to-corner to create a triangle. Compare your triangle to your partner's and to other triangles in the class. Are they congruent? Encourage the students to prove the triangles congruent using the definition of congruent triangles. Measure each side with a ruler and each angle with a protractor (measuring each side may not be necessary if students realize that everyone started with the same three strips of paper).

What was the minimum amount of information used to create these two congruent triangles? three congruent sides- this demonstrates SSS theorem of congruency Can you replicate this process in the same manner? Allow students to create another set of congruent triangles if they are not convinced. You can use the beginning of Activity Two to show this congruence. Activity Two Worksheet: Only ONE person in each group: Using the three strips of paper from Activity One, fold and cut each strip of paper in half.

Create a triangle using the one-half pieces of each of the original strips. Compare this triangle to the first one.

Describe any similarities and differences. the two triangles are not congruent, but are the same shape. These two triangles are similar. You may want to emphasize that all of the NEW triangles are congruent to each other- have students prove this to you using SSS Help students trace the new triangle and label the sides the same as in Activity One. Students will justify the similarity of the old and new triangles. Have students measure each side of the triangle and place the measure in the space requested on the worksheet.

Note that the ratios of the lengths of each pair of corresponding sides are proportional. Have students measure each pair of corresponding angles. Note that the measures of each pair of corresponding angles are congruent. The answers in #4 and #5 show that the triangles are similar.

Activity Three Worksheet: Each student will copy the two sides and included angle using patty paper. Students should now draw segment AC to create a triangle. Lead a discussion about what parts of the triangle were given and how their measures compare with everyone else's SAS. Now, students will compare their triangle to the other triangles in the group.

Have students justify that the triangles are congruent – or similar by definition they are both. Encourage them to show that the corresponding three sides of the triangles are congruent and therefore the triangles are congruent.

Ask students to locate the midpoint of AB and of BC and label these points D and E, respectively. Leap test administrator manual 2018. Draw segment DE.

Similarity Congruence Worksheets With Answers

Compare this triangle to triangle ABC. the two are similar. Use the definition of similar triangles to justify that the triangles are similar. Lead a discussion about what parts of the triangle were given and how this is a minimal amount of information needed in order to prove two triangles similar SAS. Activity Four Worksheet: Students will now trace two angles and use these to create two triangles.

These directions may be difficult for students to follow- please try to demonstrate using the overhead and transparencies. Have the students create two different triangles. Lead a discussion about why the two triangles are not congruent and that AA or AAA is not a way to prove two triangles congruent. The two triangles they create will be similar.

Give them time to measure the sides and show that the ratios of the corresponding sides are proportional. This will be a great revelation because the ratios of the corresponding sides will be different than the others they have seen in these activities (all of the former being 2:1).

Also have the students show that the three angles are congruent to each other. Lead a discussion about how the minimum amount of information needed to prove two triangles similar is that two corresponding angles must be congruent. AA By the time they finish these investigations, they will be ready to believe that the ASA theorem of congruence works, or you can show this using a demonstrations.

Congruence And Similarity Pdf

Discuss that ASA works for similarity as well and can really be the same as the AA theorem. Worksheet: Closure.

Unit 1 Transformations Congruence And Similarity Study Guide Answers

Similarity Similarity is much like congruence, except in order for polygons to be similar, they only need to have the same shape. As we did with congruence, we will study similarity in triangles to simplify things. Formally speaking, two triangles are similar when their corresponding angles are equal and their corresponding sides are proportional. For example, if triangles ABC and DEF are similar, then angle pairs AB and DE, BC and EF, and CA and FE are all equal. Also, AB/DE=BC/EF=CA/FD.

If these three ratios are equal, then the corresponding sides are said to be proportional.