Topics
6. Congruence & Triangles
topic badge
United States of AmericaVirginia
Geometry

6.04 ASA and AAS congruence criteria

Lesson
Practice
Adaptive
Worksheet

Interactive practice questions

This two-column proof shows that $\Delta RTQ\cong\Delta RSP$ΔRTQ≅ΔRSP in the attached diagram, but it is incomplete.

Statements Reasons
$\overline{PS}\cong\overline{QT}$PS≅QT Given
$\angle PSR\cong\angle QTR$∠PSR≅∠QTR Given

$\left[\text{___}\right]$[___]

 $\left[\text{___}\right]$[___]

$\Delta RTQ\cong\Delta RSP$ΔRTQ≅ΔRSP

 Angle-angle-side congruence (AAS)
triangle(PRS) and triangle(QRT) are formed by two intersecting lines whose point of intersection is vertex R. From the illustration, angle(PSR) and angle(QTR) are corresponding angles and are congruent. Sides PS and QT are congruent and are also corresponding sides of the triangles. angle(PRS) and angle(QRT) are vertical angles and are corresponding angles.

Select the correct reason to complete the proof.

$\angle PRS\cong\angle QRT$∠PRS≅∠QRT Reflexive property of congruence
A
$\angle QRT\cong\angle PRS$∠QRT≅∠PRS Vertical angles congruence theorem
B
$\angle SPR\cong\angle TQR$∠SPR≅∠TQR Third angle theorem
C
$\angle SPR\cong\angle TQR$∠SPR≅∠TQR Vertical angle congruence theorem
D
Medium
< 1min

Consider the two triangles in the diagram below:

Easy
< 1min

Consider the two triangles in the diagram below:

Easy
< 1min

Consider the two triangles in the diagram below:

Easy
< 1min
Sign up to access Practice Questions
Get full access to our content with a Mathspace account
Book a Demo
Sign up for free

Outcomes

G.TR.2

The student will, given information in the form of a figure or statement, prove and justify two triangles are congruent using direct and indirect proofs, and solve problems involving measured attributes of congruent triangles.

G.TR.2a

Use definitions, postulates, and theorems (including Side-Side-Side (SSS); Side-Angle-Side (SAS); Angle-Side-Angle (ASA); Angle-Angle-Side (AAS); and Hypotenuse-Leg (HL)) to prove and justify two triangles are congruent.

G.TR.2b

Use algebraic methods to prove that two triangles are congruent.

G.TR.2d

Given a triangle, use congruent segment, congruent angle, and/or perpendicular line constructions to create a congruent triangle (SSS, SAS, ASA, AAS, and HL).

What is Mathspace

About Mathspace