Congruence & Sequences of Transformations — Drills
Congruence & Sequences of Transformations has 5 drill skills. Each one generates fresh questions every time, with a hint and full worked steps, so you can keep practising a single skill until it settles.
What these drills cover
These questions use 8 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Corresponding sides — Sides in matching positions in two similar figures.
- Perimeter — Distance all the way around the outside.
- Rigid motion — A move that keeps every length and every angle. Slides, flips and turns are all rigid.
- Congruent — Same size and same shape. Written △ ABC ≅ △ DEF.
- Orientation — Whether the labels run clockwise or counter-clockwise around the shape.
- Dilation — A resizing from a centre point by a scale factor k.
- Transformation — A change to the function that moves or stretches its graph.
- Sequence — An ordered list of numbers. The nth one is an.
Corresp
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
△ ABC ≅ △ DEF and BC = 17. Find EF.
Worked answer
17
BC corresponds to EF.
Corresponding sides of congruent triangles are equal.
EF = 17
Problem 2
△ ABC ≅ △ DEF and BC = 5. Find EF.
Worked answer
5
BC corresponds to EF.
Corresponding sides of congruent triangles are equal.
EF = 5
Rigid
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A square of side 9 cm is translated 8 units right. Find the side length of the image.
Worked answer
9
Slides, flips and turns are rigid motions.
They change position, not size.
The side is still 9 cm.
Problem 2
A square of side 13 cm is translated 8 units right. Find the side length of the image.
Worked answer
13
Slides, flips and turns are rigid motions.
They change position, not size.
The side is still 13 cm.
Sequence
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
(3, 1) is reflected across the x-axis, then translated 5 up. Find the image.
Worked answer
(3, 4)
Reflect: (3, -1)
Translate: (3, 4)
Problem 2
(3, -1) is reflected across the x-axis, then translated 1 down. Find the image.
Worked answer
(3, 0)
Reflect: (3, 1)
Translate: (3, 0)
Solving
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
△ ABC ≅ △ DEF with AB = 5x - 9 and DE = 4x + 0. Find x.
Worked answer
9
5x - 9 = 4x + 0
1x = 9
x = 9
Check: both give 36 ✓
Problem 2
△ ABC ≅ △ DEF with AB = 4x - 4 and DE = 3x + 8. Find x.
Worked answer
12
4x - 4 = 3x + 8
1x = 12
x = 12
Check: both give 44 ✓
Orient
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A figure is reflected 1 time, each across a different line. Is the final orientation the same as the original, or reversed?
Worked answer
reversed
One reflection reverses the orientation.
1 reflections reverse it 1 time.
1 is odd, so it ends reversed.
Problem 2
A figure is reflected 2 times, each across a different line. Is the final orientation the same as the original, or reversed?
Worked answer
same
One reflection reverses the orientation.
2 reflections reverse it 2 times.
2 is even, so it ends the same.