Question

geometry
november 14, 2025
review for quiz #04
name:
period: 1 2 4 7 (circle)
before the timer is up, do at least a few problems and get a stamp for bonus points on the quiz.

1. the following triangles may be congruent. which triangle congruence shortcut is possible from the given information? circle your choice. only one choice is correct for each diagram. if there is not enough information to make one of the shortcuts, then mark

one.\
(i.)
sss sas
asa aas
none (not enough info)
(ii.)
sss sas
asa aas
none (not enough info)
(iii.)
sss sas
asa aas
none (not enough info)

1. see the marks in the diagram below. write congruence statements for them.

∠abc ≅ ∠______
____ ≅ ____
____ ≅ ____

1. given the congruence statements below, mark the diagram to show congruent parts.

lm ≅ pn
∠lmx ≅ ∠pnx
∠lxm ≅ ∠pxn

Explanation:

(i.)

Step1: Analyze triangle congruence

The diagram shows three pairs of equal sides.

Step2: Apply SSS congruence

By the Side - Side - Side (SSS) congruence shortcut, if three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.

(ii.)

Step1: Check given information

We have two sides equal (\(BC = EC\), \(AC = DC\)) but no included angle information.

Step2: Determine congruence

Since there is not enough information to apply SSS, SAS, ASA, or AAS, we mark "None".

(iii.)

Step1: Identify vertical angles

\(\angle ACB=\angle DCE\) (vertical angles are equal).

Step2: Check sides

We have \(AC = DC\) and \(BC = EC\).

Step3: Apply SAS congruence

By the Side - Angle - Side (SAS) congruence shortcut (two sides and the included angle), the triangles are congruent.

2.

Step1: Identify congruent angles

\(\angle ABC\cong\angle DFE\) (by looking at the angle markings).

Step2: Identify congruent sides

\(BC\cong EF\) (side markings), \(\angle ACB\cong\angle DEF\) (angle markings)

Answer:

(i.) SSS; (ii.) None; (iii.) SAS; 2. \(\angle ABC\cong\angle DFE\), \(BC\cong EF\), \(\angle ACB\cong\angle DEF\)