Math 7: Unit 9 Assessment Summary

Congruent and Similar Figures in Geometry

Congruence and Similarity Basics

• Congruent figures have the same size and shape.
• Similar figures have the same shape but not necessarily the same size.

Key Concepts from Assessment

1. Identifying Congruent Segments:
   • Given triangles $AABC$ and $ATRS$, determine the congruent line segments (e.g., find which segment is congruent to $AC$).
2. Solving for Unknowns in Triangles:
   • For similar triangles, such as those depicted in sections with values, use the ratio of corresponding sides to find unknowns (e.g. solve for $x$ provided proportions).
3. Angle Correspondence:
   • In triangle relationships, identify congruent angles, such as finding which angle in ABCD is congruent to $ riangle ZC$.
4. Using Given Measurements:
   • Utilize provided measurements (e.g., angle degrees and side lengths) to calculate other angles or segment lengths as needed.

Example Problem Breakdown

• Triangles ADOG and ACAT:
  • Given angles: $ riangle ZD = 35^ ext{°}$, $ZA = 85^ ext{°}$; sides: $DO = 17.8$, $CA = 15$, $AT = 7$.
  • Draw and label both triangles with all side lengths and angle measures.
  • Calculate unknown angle $G$: $180^ ext{°} - (35^ ext{°} + 85^ ext{°})$.
  • Use trigonometric ratios or geometric properties to calculate the length $OG$.

Scoring and Points

• Total sections worth points: Section assessment consists of various problems, each contributing to a total score out of 18 points.