WHAT'S INCLUDED:

This lesson is aligned with TEKS - Geometry

• G.5A: Investigate patterns to make conjectures about geometric relationships, including angles formed by parallel lines cut by a transversal, criteria required for triangle congruence, special segments of triangles, diagonals of quadrilaterals, interior and exterior angles of polygons, and special segments and angles of circles choosing from a variety of tools.

Task Card Sizes: Prints in 8.5 x 11

• (1 in 1 page)
• (2 in 1 page)
• (4 in 1 page)

Task Cards: 24 Questions:

1. What is the measure of ∠5?
   
2. Carlos says that if two lines are cut by a transversal and corresponding angles are not congruent, then the lines are not parallel. Is he correct?
   
3. Which pair is always supplementary?
   
4. Which triangle congruence postulate is used to show △ABC ≅ △DEF?
   
5. You are given two right triangles. One has legs of 3 cm and 4 cm, and the other has legs of 3 cm and 4 cm. What conjecture can you make?
   
6. Ella proves two triangles congruent by showing they both have one 90° angle, one 60° angle, and a side of 5 cm between the two angles. Which postulate did she use?
   
7. What do you call point G?
   
8. Based on the diagram, what can we conclude about the diagonals of a parallelogram?
   
9. Mira draws a quadrilateral with diagonals that intersect but do not bisect each other. What type of quadrilateral could she have drawn?
   
10. Looking at the diagram, if the sum of the other five interior angles is 600°, what is the measure of angle x?
    
11. Which segment is always the longest?
    
12. Liam draws a chord and its perpendicular bisector in a circle. What does the bisector pass through?
    
13. Can triangle congruence still be established based on the diagram, even if one triangle is rotated?
    
14. A student says: “If two lines are crossed by a transversal and alternate interior angles are not equal, the lines are still parallel.” What can you infer?
    
15. Mina uses dynamic geometry software to drag the vertices of a triangle while measuring the medians. She observes they always intersect at the same point. What conjecture can she make?
    
16. What is the value of z?
    
17. What is the measure of the inscribed angle?
    
18. Ali folds a triangle-shaped paper so that a vertex touches the midpoint of the opposite side. He notices the fold divides the triangle into two equal areas. What did he create?
    
19. Jason says that a quadrilateral with diagonals that are both congruent and bisect each other must be a square. Is his conclusion correct?
    
20. Samantha notices that every time she draws a regular polygon, the exterior angles always add up to 360°. What conjecture can she make?
    
21. During a construction activity, Ian draws a chord in a circle and then its perpendicular bisector. He sees the line goes through the center of the circle. What can he conclude?
    
22. What is point x called?
    
23. What is the measure of the intercepted arc?
    
24. What is the measure of the angle opposite the diameter?