Math Problem Statement

△GFH ≅ △PQO. What is OP?

Solution

We are given that triangles GFHPQO\triangle GFH \cong \triangle PQO, which means they are congruent. Congruent triangles have corresponding sides and angles that are equal.

From triangle GFH\triangle GFH, we know the following:

  • GF=50ftGF = 50 \, \text{ft}
  • FH=40ftFH = 40 \, \text{ft}
  • GH=56ftGH = 56 \, \text{ft}
  • G=44\angle G = 44^\circ
  • F=76\angle F = 76^\circ
  • H=60\angle H = 60^\circ

Since the triangles are congruent, the corresponding sides and angles in PQO\triangle PQO will be equal to those in GFH\triangle GFH. This gives us the following correspondences:

  • GFPOGF \cong PO
  • FHOQFH \cong OQ
  • GHPQGH \cong PQ

We are tasked with finding OPOP. Since GF=50ftGF = 50 \, \text{ft} and GFPOGF \cong PO, we can directly conclude that:

OP=50ftOP = 50 \, \text{ft}

Would you like further clarification or additional details?

Here are 5 related questions to expand on this topic:

  1. How can you use congruent triangles to solve real-world problems involving measurements?
  2. What is the significance of corresponding angles in congruent triangles?
  3. How do the properties of congruent triangles help in simplifying geometric proofs?
  4. Can you find the perimeter of PQO\triangle PQO using the given information?
  5. How do you determine if two triangles are congruent using the SSS (Side-Side-Side) or SAS (Side-Angle-Side) postulate?

Tip: Always label the sides and angles carefully when working with congruent triangles to ensure that corresponding parts are matched correctly!

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Math Problem Analysis

Mathematical Concepts

Geometry
Congruent Triangles
Corresponding Parts

Formulas

None required (congruence property)

Theorems

Triangle Congruence Theorem

Suitable Grade Level

Grades 9-11