Using Congruent Triangles
Today you will need:
Grab a warm-up from the wooden desk and get started! :-)
Goals:
Warm-up #1
Warm-up #1 KEY
SSS
SAS
Similar by AA
neither
AAS
neither
Warm-up #2
Draw and label two triangles based on the given congruence statements.
Warm-up #2
Lazy Lizard: Translate the original lizard so the point at the tip of its nose is located at (24, 20) making the lizard appear to be sunbathing on the rock.
Lunging Lizard: Rotate the lizard 90 degrees about point A(12, 7) so it looks like the lizard is diving into the puddle of mud.
Leaping Lizard: Reflect the lizard about the given line y=1/2x+16 so it looks like the lizard is doing a backflip over the cactus.
Warm-up #1
Use patty paper to identify a sequence of transformations that will carry triangle RST onto triangle R’S’T’.
Warm-up #2
Dilations!
What do you notice?
K =2
Pre-Image | Image |
T (-1, 1) | T’ (-2, 2) |
R (2, 2) | R’ (4, 4) |
S (0, -1) | S’ (0, -2) |
How can you use congruent triangles to make an indirect measurement?
How can you use congruent triangles to make an indirect measurement?
Tell me what you learned!
3. How can you use congruent triangles to make an indirect measurement?
4. Why do you think the types of measurements described in explorations 1 and 2 are called indirect measurements?
Resources
Activites for Extra Practice:
Congruent Triangles Digital Escape Room
Congruent Triangles Scavenger Hunt
Mod 4 Standards
G.CO.10 Prove and apply theorems about triangles. Theorems include but are not restricted to the following: measures of interior angles of a triangle sum to 180 degrees; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.
G.CO.7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
G.CO.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motion.
G.CO.11 Prove and apply theorems about parallelograms. Theorems include but are not restricted to the following: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.
Delta Math