Congruent Triangles Worksheets - Free Printable

It looks like you've uploaded a worksheet titled "Congruence Statements" that includes several geometry problems involving triangle congruence. Since I can't view images directly, I'll help you solve the problems based on typical content found in such worksheets. Below is a step-by-step explanation and solution for each type of problem commonly found on this kind of worksheet.

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Problem 1: Complete each congruence statement

This section usually asks you to write a correct congruence statement based on given information (e.g., sides and angles marked as congruent).

#### Example:
> Given: $ \triangle ABC \cong \triangle DEF $

Then, the corresponding parts are:
- $ AB \cong DE $
- $ BC \cong EF $
- $ AC \cong DF $
- $ \angle A \cong \angle D $
- $ \angle B \cong \angle E $
- $ \angle C \cong \angle F $

So, if asked to complete:
1. $ \triangle ABC \cong \triangle ___ $
- Answer: $ \triangle DEF $

2. $ \angle B \cong \angle ___ $
- Answer: $ \angle E $

3. $ \overline{AC} \cong \overline{___} $
- Answer: $ \overline{DF} $

4. $ \angle C \cong \angle ___ $
- Answer: $ \angle F $

5. $ \overline{AB} \cong \overline{___} $
- Answer: $ \overline{DE} $

6. $ \angle A \cong \angle ___ $
- Answer: $ \angle D $

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Problem 2: Complete each congruence statement using the diagram

You’ll have diagrams with two triangles, and some sides or angles marked as congruent. You need to determine which triangle congruence postulate applies (SSS, SAS, ASA, AAS, HL) and write the correct congruence statement.

Let’s assume the following common types:

#### Diagram A:
Two triangles: $ \triangle ABC $ and $ \triangle DEF $
- $ AB = DE $
- $ BC = EF $
- $ \angle B = \angle E $

This suggests SAS (Side-Angle-Side), so:
$$
\triangle ABC \cong \triangle DEF
$$

#### Diagram B:
$ \triangle XYZ $ and $ \triangle MNO $
- $ \angle X = \angle M $
- $ \angle Y = \angle N $
- $ XY = MN $

This is ASA, so:
$$
\triangle XYZ \cong \triangle MNO
$$

#### Diagram C:
Right triangles: $ \triangle PQR $ and $ \triangle STU $
- Right angles at $ Q $ and $ T $
- $ PQ = ST $
- $ PR = SU $

This is HL (Hypotenuse-Leg), so:
$$
\triangle PQR \cong \triangle STU
$$

#### Diagram D:
$ \triangle JKL $ and $ \triangle MNP $
- $ JK = MN $
- $ KL = NP $
- $ JL = MP $

All three sides equal → SSS
$$
\triangle JKL \cong \triangle MNP
$$

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Problem 3: If the triangles $ \triangle ABC $ and $ \triangle DEF $ are congruent, what is the corresponding part of $ \angle D $?

Given: $ \triangle ABC \cong \triangle DEF $

The order matters! So:
- $ A \leftrightarrow D $
- $ B \leftrightarrow E $
- $ C \leftrightarrow F $

Therefore, $ \angle D $ corresponds to $ \angle A $

Answer: $ \angle A $

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General Tips:

1. Order Matters: In congruence statements, the order of vertices indicates corresponding parts.
2. Use Markings: Look at tick marks on sides and arcs on angles to identify congruent parts.
3. Postulates: Use SSS, SAS, ASA, AAS, or HL to justify congruence.
4. Corresponding Parts: Once triangles are congruent, all corresponding parts (sides and angles) are congruent (CPCTC: Corresponding Parts of Congruent Triangles are Congruent).

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Final Answers (Example-Based):

1. $ \triangle ABC \cong \triangle DEF $
2. $ \angle B \cong \angle E $
3. $ \overline{AC} \cong \overline{DF} $
4. $ \angle C \cong \angle F $
5. $ \overline{AB} \cong \overline{DE} $
6. $ \angle A \cong \angle D $

7. $ \triangle ABC \cong \triangle DEF $ (by SAS)
8. $ \triangle XYZ \cong \triangle MNO $ (by ASA)
9. $ \triangle PQR \cong \triangle STU $ (by HL)
10. $ \triangle JKL \cong \triangle MNP $ (by SSS)

11. The corresponding part of $ \angle D $ is $ \angle A $

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If you can describe the specific diagrams or provide details about the markings (like tick marks, right angles, etc.), I can give more accurate answers tailored to your image. Let me know!