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The image shows two geometry problems from a Grade 9 mathematics worksheet.

### Question 2:
The task is to prove that triangles \( \triangle ABD \) and \( \triangle ACD \) are congruent, using a diagram of a rectangle.

Your solution includes the following points:
- \( \overline{AB} = \overline{CD} \) and \( \overline{AD} = \overline{BC} \), because they are opposite sides of a rectangle.
- \( \angle ABO = \angle ACO \) because angles in a rectangle are 90° (right angles).
- \( \overline{BD} \) is a common side between the two triangles.
- Using the SAS (Side-Angle-Side) congruence postulate, you conclude that \( \triangle ABD \cong \triangle ACD \).

### Question 3:
A quadrilateral \( QMNP \) is given with two angles, \( \angle Q = 83^\circ \) and \( \angle P = 41^\circ \). You are likely required to find the other angles or determine if the quadrilateral is a specific type based on angle measures.

Would you like help with any specific part of these questions or need detailed explanations on how to proceed?

Here are some related questions for further understanding:
1. How do you determine the remaining angles in quadrilateral \( QMNP \)?
2. What is the role of the diagonals in proving congruence in Question 2?
3. Can you list other congruence postulates besides SAS?
4. How can we calculate angle \( \angle M \) or \( \angle N \) in Question 3?
5. How do congruent triangles help in determining properties of rectangles?

**Tip:** In geometry, always remember to label known and unknown parts of a figure to help in solving problems systematically.

Prove that triangle ABD is congruent to triangle ACD (in the context of a rectangle). Additionally, determine the unknown angles in quadrilateral QMNP given that angle Q = 83° and angle P = 41°.

Learn how to prove the congruence of triangles ABD and ACD using the SAS postulate, and how to calculate the unknown angles in quadrilateral QMNP with given angles. This problem is suitable for Grade 9 students studying congruence and quadrilateral properties.

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