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
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What is known about angle XMN and XNM given that MN 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 DZX and DXZ given that ZX forms a diameter? |
| DZX and DXZ add to 360º |
| DZX and DXZ add to 90º |
| Nothing, DZX and DXZ are not subtended by the same arc |
| DZX is twice DXZ |
| DZX is the same as DXZ |
| DZX and DXZ add to 180º |
| What is known about angle BNP and BPN given that NP forms a diameter? |
| BNP is half BPN |
| Nothing, BNP and BPN are not subtended by the same arc |
| BNP is twice BPN |
| BNP and BPN add to 180º |
| BNP is the same as BPN |
| BNP and BPN add to 90º |
| What is known about angle ZBR and ZRB given that BR forms a diameter? |
| ZBR and ZRB add to 90º |
| ZBR is the same as ZRB |
| ZBR and ZRB add to 360º |
| Nothing, ZBR and ZRB are not subtended by the same arc |
| ZBR is twice ZRB |
| ZBR is half ZRB |
| What is known about angle PCR and PRC given that CR forms a diameter? |
| PCR is half PRC |
| PCR and PRC add to 90º |
| Nothing, PCR and PRC are not subtended by the same arc |
| PCR and PRC add to 360º |
| PCR is twice PRC |
| PCR is the same as PRC |
| What is known about angle XBR and XRB given that BR forms a diameter? |
| XBR and XRB add to 360º |
| XBR and XRB add to 180º |
| XBR is half XRB |
| XBR is the same as XRB |
| XBR is twice XRB |
| XBR and XRB add to 90º |
| What is known about angle CRB and CBR given that RB forms a diameter? |
| CRB is half CBR |
| Nothing, CRB and CBR are not subtended by the same arc |
| CRB and CBR add to 360º |
| CRB is the same as CBR |
| CRB and CBR add to 90º |
| CRB and CBR add to 180º |
| What is known about angle BXD and BDX given that XD forms a diameter? |
| BXD is half BDX |
| BXD is twice BDX |
| BXD and BDX add to 360º |
| BXD and BDX add to 90º |
| Nothing, BXD and BDX are not subtended by the same arc |
| BXD and BDX add to 180º |