This math topic focuses on the geometry of circles, specifically problems involving inscribed triangles with diameters and the relationships of their angles. Students are tasked with determining properties and relationships of angles subtended by diameters in various geometric configurations. The topic also challenges learners to deepen their understanding of the circle geometry, including how angles in inscribed triangles relate to one another and the circle's diameter. Each problem presents different cases of inscribed angles and related angle properties, crucial for learning intermediate level geometry.
Work on practice problems directly here, or download the printable pdf worksheet to practice offline.
Practice:
Inscribed Triangle on Diameter - Missing Angle Rule
Complete these online problems with 80% or 4 correct answers in a row. Results are immediate.
What is known about angle RXY and RYX given that XY forms a diameter?
Geometry of Circles - Inscribed Triangle on Diameter - Missing Angle Rule Worksheet
| Math worksheet on 'Geometry of Circles - Inscribed Triangle on Diameter - Missing Angle Rule (Level 1)'. Part of a broader unit on 'Geometry - Intermediate - Intro' Learn online: app.mobius.academy/math/units/geometry_intermediate_intro/ |
| What is known about angle MDX and MXD given that DX forms a diameter? |
| MDX and MXD add to 180º |
| MDX is the same as MXD |
| MDX is twice MXD |
| Nothing, MDX and MXD are not subtended by the same arc |
| MDX and MXD add to 90º |
| MDX is half MXD |
| What is known about angle XRZ and XZR given that RZ forms a diameter? |
| XRZ is the same as XZR |
| XRZ and XZR add to 360º |
| XRZ and XZR add to 90º |
| XRZ is half XZR |
| XRZ and XZR add to 180º |
| Nothing, XRZ and XZR are not subtended by the same arc |
| What is known about angle NPB and NBP given that PB forms a diameter? |
| Nothing, NPB and NBP are not subtended by the same arc |
| NPB and NBP add to 360º |
| NPB and NBP add to 180º |
| NPB is the same as NBP |
| NPB is twice NBP |
| NPB and NBP add to 90º |
| What is known about angle NZM and NMZ given that ZM forms a diameter? |
| NZM and NMZ add to 180º |
| Nothing, NZM and NMZ are not subtended by the same arc |
| NZM is the same as NMZ |
| NZM is twice NMZ |
| NZM and NMZ add to 90º |
| NZM is half NMZ |
| What is known about angle MBZ and MZB given that BZ forms a diameter? |
| MBZ is half MZB |
| MBZ and MZB add to 360º |
| MBZ and MZB add to 90º |
| Nothing, MBZ and MZB are not subtended by the same arc |
| MBZ is the same as MZB |
| MBZ and MZB add to 180º |
| What is known about angle NDP and NPD given that DP forms a diameter? |
| NDP is twice NPD |
| NDP and NPD add to 180º |
| NDP and NPD add to 360º |
| NDP is half NPD |
| Nothing, NDP and NPD are not subtended by the same arc |
| NDP and NPD add to 90º |
| What is known about angle PDY and PYD given that DY forms a diameter? |
| PDY is twice PYD |
| PDY and PYD add to 90º |
| PDY and PYD add to 180º |
| PDY is the same as PYD |
| PDY and PYD add to 360º |
| Nothing, PDY and PYD are not subtended by the same arc |