Track quiz
Twelve quick questions. Use the table if you get stuck.
| Idea | What to remember |
|---|---|
| Landing one on the other | Congruent figures land exactly, after any slide, turn or flip. |
| Slide, turn, flip | No side or corner changes. |
| A bigger copy | Same corners, longer sides. Not congruent. |
| One line, one corner | Compare length or degrees. Tilt does not matter. |
| Three sides (SSS) | Three equal pairs of sides make congruent triangles. |
| Two sides and the angle between (SAS) | The angle must sit between the sides. |
| Two angles and a side (ASA, AAS) | Find the third angle. Match the side. |
| Three angles (AAA) | Same shape. Size stays open. |
| Writing a congruence | In ΔABC ≅ ΔXYZ, the letters match in order. Δ means triangle. ≅ means is congruent to. A matches X, B matches Y, and C matches Z. Matching sides are equal. Matching angles are equal. |
| RHS | RHS stands for right angle, hypotenuse, side. Take two right-angled triangles. Suppose their hypotenuses are equal. Suppose one more side is equal. Then they are congruent. The hypotenuse is the side across from the right angle. |
| Equal sides, equal angles | Draw the altitude from the top of an isosceles triangle. An altitude runs from a corner, square to the opposite side. It cuts the triangle into two right-angled triangles. They are congruent by RHS, as shown below. So the angles across from the equal sides are equal. Any two sides of an equilateral triangle are equal. So all three angles are equal. Each is 60°, because they add to 180°. |
| Twins in a figure | To prove two triangles congruent, find three marked facts. Match them to SSS, SAS, ASA, AAS or RHS. The facts must fit one test exactly. In SAS, the angle sits between the two sides. A side that two triangles share counts as an equal pair. |
You slide, turn and flip a paper triangle on a drawn one. It still misses by 4 mm. Are they congruent?
A shape is turned, then flipped over. Which of its sides change length?
A drawing is copied at 140%. Every corner of the copy matches. Is the copy congruent?
One angle has arms 20 mm long. Another has arms 45 mm long. Both measure 50°. Are they congruent?
Two triangles both have sides of 52, 39 and 68 mm. Are they congruent?
Two triangles share a 60 mm side and a 45 mm side. Each has 35° at one end of the 60 mm side. The 45 mm side faces it. Must they be congruent?
A triangle has angles of 50° and 75°. What is its third angle?
Two triangles have corners of 40°, 60° and 80°. Are they congruent?
ΔPQR ≅ ΔUVT. Which side matches QR?
Two right-angled triangles have equal hypotenuses of 15 cm. One leg of each is 9 cm. What can you say?
An isosceles triangle has a top angle of 70°. What is each base angle?
AB = AC, and AD bisects angle A, with D on BC. Which condition shows ΔABD ≅ ΔACD?
Chapter 1 of Part II is Geometric Twins. Try its exercises to practise these tests.
Next: Operations with Integers. Add, subtract, multiply and share on a number line. It runs both ways.