Congruence Clues Practice Worksheet
Congruence Clues Practice
8th Grade Math • Targeted AIS Skill Builder (Unit 2, Lesson 9)
Name:
Date:
AIS STRATEGY: Matching Order Tells the Whole Story
What does Congruent (\(\cong\)) mean?
Two figures have the exact same shape and size. All matching sides and matching angles are equal.
Follow the Letter Order:
If \(\triangle \mathbf{A}\mathbf{B}\mathbf{C} \cong \triangle \mathbf{D}\mathbf{E}\mathbf{F}\), then:
\(\angle A \leftrightarrow \angle D\) | \(\angle B \leftrightarrow \angle E\) | \(\overline{AB} \leftrightarrow \overline{DE}\)
Skill 1
Matching Corresponding Parts from the Statement
Use the letter order in the formal statement to match the corresponding parts without looking at a picture.
Given: \(\triangle JKL \cong \triangle XYZ\)
Vertex J corresponds to:
Side \(\overline{KL}\) corresponds to side:
Angle \(\angle L\) corresponds to angle:
Given: \(\triangle PQR \cong \triangle MWT\)
Side \(\overline{PR}\) corresponds to side:
Angle \(\angle Q\) corresponds to angle:
Side \(\overline{PQ}\) corresponds to side:
Skill 2
Visual Identification & Tracing Congruence
Notice how figures may be rotated or flipped. Use side lengths and angle sizes to find the perfect match.
Problem 1: Look at the target triangle \(\triangle ABC\). Which of the three options (Figure 1, 2, or 3) is congruent to \(\triangle ABC\)?
Target Triangle A C B 6 9 11 \(\triangle ABC\)
Figure 1 D E F 6 9 11 \(\triangle DEF\)
Figure 2 G H I 5 8 10 \(\triangle GHI\)
Figure 3 J K L 8 8 9 \(\triangle JKL\)
(a) Which figure is congruent to \(\triangle ABC\)?
Answer: Figure
(b) Write the formal congruence statement:
\(\triangle ABC \cong \triangle\)
(c) How do you know they are congruent?
(Mention side lengths or tracing paper alignment)
Unit 2: Geometric Foundations • Lesson 9: Congruent Triangles Page 1 of 2
Part B
Mixed Practice & Corresponding Parts Analysis
AIS Guided Practice
Problem 2: Complete Parts Mapping Step-by-Step Match
The two triangles below are congruent. Triangle 2 has been rotated.
M U N 7 cm 12 cm 14 cm \(\triangle MUN\)
\(\cong\) congruent to
Y X Z 12 cm 7 cm 14 cm \(\triangle XYZ\)
1. Congruence Statement
Match corresponding vertices in order:
\(\triangle MUN \cong \triangle\)
2. List 3 Congruent Sides
\(\overline{MU} \cong\)
\(\overline{UN} \cong\)
\(\overline{MN} \cong\)
3. List 3 Congruent Angles
\(\angle M \cong\)
\(\angle U \cong\)
\(\angle N \cong\)
Problem 3: Missing Angles & Algebra Connection Lesson Slide Application
The two triangles shown below are congruent: \(\triangle EFG\) and \(\triangle RST\).
E F G \(41^\circ\) \(114^\circ\) \(25^\circ\)
R T S \(114^\circ\)
(a) Complete the formal congruence statement:
\(\triangle EFG \cong \triangle\)
(b) Which angle corresponds to \(\angle E\) (\(41^\circ\))?
Corresponding Angle: so its measure is
(c) Find the value of \(x\):
If \(m\angle T = 4x - 7\), and \(\angle T\) corresponds to \(\angle E\) (\(41^\circ\)), set up and solve the equation:
Equation: 4x - 7 = ______
Value of \(x\) =
AIS Self-Check: Did you check that matching letters are in the exact same order?
Yes, fully aligned! Need extra review
Unit 2: Geometric Foundations • Lesson 9: Congruent Triangles Page 2 of 2
