Congruence: Theorems about Triangles (CCSS.G-CO.9)
Common Core High School Geometry · Learn by Concept
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Common Core High School Geometry › Congruence: Theorems about Triangles (CCSS.G-CO.9)
Triangle with vertices $A(0,0)$, $B(6,0)$, and $C(3,4)$. What are the coordinates of the midpoint of $AB$?
$(6,0)$
$(0,3)$
$(3,0)$
$(3,4)$
Explanation
Use the midpoint formula: average the $x$-coordinates and the $y$-coordinates. For $A(0,0)$ and $B(6,0)$, midpoint $=\left(\frac{0+6}{2},\frac{0+0}{2}\right)=(3,0)$. The distractor $(0,3)$ swaps the coordinates instead of averaging correctly.
In $\triangle ABC$, $\angle ABC$ measures $78^\circ$. What is the measure of $\angle ABC$ after it is bisected?
$39^\circ$
$78^\circ$
$38^\circ$
$90^\circ$
Explanation
An angle bisector divides an angle into two equal angles, so each part is $\frac{78^\circ}{2}=39^\circ$. The distractor $38^\circ$ comes from misdividing by 2.
Two lines intersect to form vertical angles. If one of the angles measures $112^\circ$, what is the measure of its vertical angle?
$68^\circ$
$112^\circ$
$90^\circ$
$56^\circ$
Explanation
Vertical angles are congruent, so the opposite (vertical) angle is also $112^\circ$. The distractor $68^\circ$ is the supplement (linear pair), not the vertical angle.
Two parallel lines $l$ and $m$ are cut by a transversal. If an angle formed at line $l$ measures $67^\circ$, what is the measure of the corresponding angle formed at line $m$?
$113^\circ$
$33^\circ$
$67^\circ$
$47^\circ$
Explanation
When a transversal crosses parallel lines, corresponding angles are congruent. Therefore, the corresponding angle is also $67^\circ$. The distractor $113^\circ$ is the supplement (a linear-pair angle), not the corresponding angle.