Idea 23of 24Builds onCongruent means an exact copy
Same angles can differ in size
Is matching angles enough to make two triangles congruent?
Today you'll discover
- what matching angles do and do not tell you
- why three matching sides are enough
- which measures make an exact copy
Think firstBoth have angles 37°, 90° and 53°
Both triangles have angles of 37°, 90° and 53°. Are they congruent?
Decide first, then press Next. Compare the sides, not just the angles.
A small right triangle P and a bigger one Q, both with angles 37°, 90° and 53°. Their sides are then shown: 4, 3 and 5 cm for P, 8, 6 and 10 cm for Q. A dashed copy of P covers only part of Q. Then two triangles with the same three sides, one upside down, and a copy of the first that fits the second exactly.
See the whole ideathe big idea and the key word, in one place
The big idea
Three matching sides make triangles congruent; three matching angles do not, because sizes can differ.
Compare themSame three sides: always congruent, because the angles follow. Same three angles: same shape, but one can be bigger, so not always congruent.
Copy a triangleTo construct a congruent copy, measure the three sides, then build them with a ruler and compass.
Key word
- matching sides
- sides in the same place on two shapes that have the same length
Ready to use it?
- Decide which measurements make an exact copy of a triangle.