Geometric Proofs Match Warmup
Geometry Proof Foundations • Visual Warm-Up
Proof Reasons Match Warmup
Name:
Date:
Period:
Directions: Match each diagram and geometric scenario (#1–12) to the correct reason from the Bank. Write the letter in each blank box.
Bank of Justifications Letters A through L are used once
A Reflexive Property
D ASA Postulate
G Def. of Vertical \(\angle\)s
J Def. of Bisect
B SSS Postulate
E AAS Theorem
H Vertical \(\angle\)s are \(\cong\)
K Def. of Perpendicular
C SAS Postulate
F Def. of Midpoint
I CPCTC
L All Right \(\angle\)s are \(\cong\)
#1
B D A C
In \(\triangle ABD\) & \(\triangle CBD\), stating that shared segment \(\overline{BD} \cong \overline{BD}\).
#2
m n 90°
Given line \(m \perp\) line \(n\), concluding they intersect to form right angles.
#3
A M B
Point \(M\) is the midpoint of \(\overline{AB}\); deducing that \(\overline{AM} \cong \overline{MB}\).
#4
Proving congruence using two sides and the included angle: \(\overline{AB}\), \(\angle B\), and \(\overline{BC}\).
#5
1 3
Lines intersect forming opposite angles \(\angle 1\) and \(\angle 3\); concluding that \(\angle 1 \cong \angle 3\).
#6
B D
Ray \(\vec{BD}\) cuts \(\angle ABC\) into two congruent parts: \(m\angle ABD = m\angle DBC\).
#7
Proving triangles congruent given three side pairs: \(\overline{GH}\cong\overline{KL}\), \(\overline{HJ}\cong\overline{LM}\), \(\overline{GJ}\cong\overline{KM}\).
#8
∠2 ∠4
Classifying \(\angle 2\) and \(\angle 4\) as non-adjacent opposite angles formed by intersecting lines.
#9
Proving triangles congruent given two angles and the included side: \(\angle T\), \(\overline{TU}\), and \(\angle U\).
#10
∠R=90° ∠S=90°
Given that \(\angle R\) and \(\angle S\) are both right angles, concluding that \(\angle R \cong \angle S\).
#11
Proving congruence given two angles and a consecutive non-included side: \(\angle P\), \(\angle Q\), and \(\overline{QR}\).
#12
≅ CPCTC →
Having established \(\triangle JKL \cong \triangle MNP\), deducing next that corresponding side \(\overline{JL} \cong \overline{MP}\).
Proof Reasons Answer Key
Teacher Resource • Answer Key & Facilitation Guide
Proof Reasons Answer Key
Total Points: 12
Geometry Proof Foundations
Quick Scan:
#1: A #2: K #3: F #4: C #5: H #6: J #7: B #8: G #9: D #10: L #11: E #12: I
#1 A
Reflexive Property
Any geometric entity is congruent to itself (\(\overline{BD} \cong \overline{BD}\) or \(\angle B \cong \angle B\)). Essential for overlapping shared sides in triangle proofs.
#2 K
Definition of Perpendicular
By definition, perpendicular lines (\(\perp\)) intersect at \(90^\circ\) angles. Used to turn the given \(\perp\) symbol into right angles in proof step 2.
#3 F
Definition of Midpoint
A midpoint is explicitly a point that cuts a segment into two congruent halves (\(\overline{AM} \cong \overline{MB}\)). Distinguish from bisecting rays/lines.
#4 C
SAS Congruence Postulate
Side-Angle-Side requires the congruent angle (\(\angle B\)) to be strictly included (physically between) side \(\overline{AB}\) and side \(\overline{BC}\).
#5 H
Vertical Angles are Congruent
The Vertical Angles Theorem guarantees equal measures (\(\angle 1 \cong \angle 3\)). Students often mistakenly write the definition here—remind them equality is a theorem.
#6 J
Definition of Bisect
An angle bisector is a ray/line that divides an angle into two equal parts (\(m\angle ABD = m\angle DBC\)). Applies to segments or angles.
#7 B
SSS Congruence Postulate
When all three corresponding side pairs of two triangles are congruent, the triangles are congruent without needing any angle measures.
#8 G
Definition of Vertical Angles
Defines the geometrical position: two non-adjacent angles whose sides form two pairs of opposite rays. Does not assert congruence.
#9 D
ASA Congruence Postulate
Angle-Side-Angle requires the side (\(\overline{TU}\)) to connect the two given angle vertices (\(\angle T\) and \(\angle U\)) as an included side.
#10 L
All Right Angles are Congruent
The Right Angle Congruence Theorem states that since every right angle measures \(90^\circ\), any two right angles are congruent (\(\angle R \cong \angle S\)).
