Math Problem Statement

Determine the solution for the intersection of planes in a prism and evaluate the correctness of statements regarding planes and points.

Solution

You've uploaded two images. I will analyze them and provide solutions to the mathematical problems. Let me process the contents and give you detailed explanations.### Analysis of the First Image (Latihan Mandiri 3 no 2)

Problem:

The problem involves finding the intersection between the planes PQVWPQVW and QRWTQRWT in a rectangular prism.

Key Concepts:

  1. Planes in geometry are flat surfaces defined by three or more points.
  2. The intersection of two planes in a rectangular prism usually forms a line.
  3. The given planes:
    • Plane PQVWPQVW: Defined by points P,Q,V,WP, Q, V, W.
    • Plane QRWTQRWT: Defined by points Q,R,W,TQ, R, W, T.

Solution:

To determine the intersection:

  • Both planes share points QQ and WW.
  • The line of intersection is line QWQW since it's the common edge shared by these two planes.

Final Answer: Option (a) garis QW


Analysis of the Second Image (Latihan Mandiri 3 no 3)

Problem:

We are tasked to determine which statements are correct regarding point AA, line gg, and planes α\alpha and β\beta. The problem provides four statements and asks for the correct combination.

Key Information:

  1. AA is the intersection point of line gg and line hh.
  2. The statements involve checking whether AA lies on plane α\alpha, plane β\beta, or both, and if gg lies on either plane.

Evaluation of Statements:

  1. (i) Point AA lies on plane α\alpha.

    • From the diagram, AA is on the intersection of α\alpha and β\beta, so this is true.
  2. (ii) Point AA lies on plane β\beta.

    • Same as above, AA is shared by

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Math Problem Analysis

Mathematical Concepts

Geometry
Planes and Lines
Intersection of Geometric Shapes

Formulas

-

Theorems

Intersection of Planes
Definition of a Line Segment

Suitable Grade Level

Grades 10-12