Final: The Roof Frame

Part of the Congruence & Proof section of Coddy's Geometry journey. Lesson 63 of 63.

A roof frame is the triangle LGB: two rafters LG and LB meet at the ridge L, and GB is the base. A level beam HS joins the rafters, parallel to GB, with H on LG and S on LB.

Along the rafter LG, LH = 4 and HG = 8. The beam HS is 3 long. How long is the base GB?

Challenge

In the roof frame △LGB, H is on LG and S is on LB, with HS ∥ GB. LH = 4, HG = 8 and HS = 3. Find GB, then press Check.

Try it yourself

$Find the marked part of the figure$

Find the marked part of the figure

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Congruence & Proof

2Congruent Triangles

Same Size, Same Shape Matching Sides Matching Angles What Congruence Gives Recap: Matching Parts

5ASA and AAS

The Side Between The ASA Rule The AAS Rule ASA or AAS?Recap: ASA and AAS

8Proofs with Vertical Angles

Vertical Angles in Proofs The Bowtie Bowtie with ASA Linear Pairs in Proofs Recap: Vertical Angles

11Similarity Proofs

3SSS

Three Sides Fix It The SSS Rule A Shared Side SSS with a Shared Side Recap: SSS

6HL for Right Triangles

Hypotenuse and Legs The HL Rule Why HL Works HL with a Shared Leg Recap: HL

9Proofs with Parallel Lines

Parallel Angles as Reasons Alternate Angles in a Proof Corresponding Angles in Proofs Parallel or Not?Recap: Parallel Proofs

12Final Challenges

Final: The Kite Diagonals Final: Overlapping Triangles Final: Enough to Find It?Final: The Height BisectsFinal: The Roof Frame