During a deep space expedition, Emek and Tara received conflicting navigation data displayed as layered geometric constructions on the ship's guidance system. Each proposed flight corridor appeared reasonable at first, but only one satisfied every relationship involving angles, distances, parallel lines, and intersecting paths. They carefully compared the geometric deductions, testing each conclusion for consistency rather than relying on a single diagram. One proposed route produced a contradiction, revealing it to be unsafe. After identifying the only valid flight corridor, they updated the navigation system and guided the vessel safely past a hazardous region, allowing the mission to continue as planned.
Challenges
Challenge 1 of 5
Challenges
Challenge 1 of 4
Hint
Alternate interior angles formed by parallel lines are equal.
Two parallel boundary lines on the navigation grid are crossed by the same flight path. A pair of alternate interior angles are labeled (3x + 8)° and (5x - 28)°. Which conclusion is consistent with the parallel-line condition?
x = 10, and each angle measures 38°x = 18, and each angle measures 62°x = 20, and each angle measures 68°x = 36, and the angles measure 116° and 152°Correct! Equating the angle expressions gives x = 18 and an angle measure of 62°.
Set the two alternate interior angle expressions equal, then check the resulting angle measure.
Next🎉 Congrats! You got this question!
Hint
Find the horizontal and vertical changes, then use the distance formula.
Two navigation checkpoints are located at A(-2, 1) and B(4, 9) on the coordinate grid. What is the straight-line distance from A to B, in grid units?
Correct! The two checkpoints are 10 grid units apart.
Use the changes in both coordinates as the legs of a right triangle.
Next🎉 Congrats! You got this question!
Hint
For a valid triangle, the sum of any two side lengths must be greater than the third side.
The guidance system proposes four triangular flight corridors. Which proposal must be rejected because its three side lengths cannot form a triangle?
Corridor A: 7 units, 10 units, and 12 unitsCorridor B: 8 units, 15 units, and 17 unitsCorridor C: 9 units, 11 units, and 18 unitsCorridor D: 6 units, 10 units, and 17 unitsCorrect! Since 6 + 10 is less than 17, Corridor D cannot form a triangle.
Check the two shorter sides of each proposed corridor and compare their sum with the longest side.
Next🎉🎉🎉🎉🎉🎉🎉🎉
🎉 Congrats! You finished this challenge set!
