L4 · Congruence: same size, same shape
“I can decide whether two shapes are congruent by superimposing them - placing one exactly on the other, turning or flipping if needed - and I can explain how congruent differs from merely similar or merely equal in area.”
Shape P is the triangle with vertices (1, 1), (4, 1), (1, 3). Shape Q is the triangle with vertices (6, 2), (9, 2), (9, 4). Are they congruent? Step 1: Measure P by grid counting. From (1, 1) to (4, 1) is 3 units; from (1, 1) to (1, 3) is 2 units; the slanted side joins (4, 1) to (1, 3). Step 2: Measure Q. From (6, 2) to (9, 2) is 3 units; from (9, 2) to (9, 4) is 2 units; the slanted side joins (6, 2) to (9, 4) - the same slant (3 across, 2 up) as P's. Step 3: Trace P, lift it, and flip it over. The flipped tracing lands exactly on Q - every side and every angle coincides. So P and Q ARE congruent. The flip was allowed: superimposing includes sliding, turning, and flipping, just like picking up a paper cut-out.
When you superimpose two shapes to test congruence, you are allowed to...
Shape R is the triangle (2, 5), (6, 5), (2, 8) - legs 4 and 3. Shape S is the triangle (3, 1), (7, 1), (7, 4) - legs 4 and 3, right angle at (7, 1). Congruent to R? -> Yes - same legs (4 and 3) with the right angle, so a slide and a flip superimpose R exactly on S.
"Two rectangles both measure 5 units by 3 units. Slide one onto the other: every side and angle coincides, so the rectangles are ___" -> congruent
10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.