Euclidean geometry: transformations and congruence

Practice 5 items →

Rigid motions preserve distance and angle; dilations preserve angle only. Students apply and compose translation, reflection, rotation, and dilation rules, name the motion between figures, and justify congruence (SSS, SAS, ASA, AAS, HL) and similarity (AA, SAS, SSS).

Specification · for a parent or teacher

Part no.: transformations-congruence
Course: High School Math 1 · Unit 16
Realm: Shapes
Difficulty: 4 of 4 — Grade 7 / Math 1 core. Structure, models, proofs on the grid.
Qty: 5 items

Part no. is the node's id; the realm is the kind of math; qty is how many practice items it carries.

Students can

apply and compose the seven rules; name the motion that maps one figure to another; state which congruence or similarity shortcut applies and why SSA fails; find a scale factor.

Ready when

a triangle mapped by a 90° rotation then a dilation, with congruence vs similarity named.

Formulas

Rotate 90° CCW

(x,y) \mapsto (-y, x)

Reflect over y = x

(x,y) \mapsto (y, x)

Dilate by k

(x,y) \mapsto (kx, ky)

Watch for

$90^\circ$ rotation as $(x,y)\mapsto(-x,y)$ ; SAS~ using two sides and a non-included angle.

Before · requires

Coordinate geometrycoordinate-geometry · Math 1
Polygonspolygons-angle-theorems · Math 1

After · used by

— none

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